As well as everything the others have said above, he should obviously take a decent test ride on the bike.
I test rode a DL1000 with around 12k miles on the clock from Orwell Motorcycles (near you in Ipswich, you no doubt already know) and after about 40 minutes of riding it started spewing coolant out of the radiator. Clearly there was a split there which had opened up when the radiator started getting hotter!
If the bike he's going to see doens't have the skid plate or a radiator guard (or even a "mudguard extender") he should check the radiator thouroughly for any signs of damage from debris impact as this is quite common on "unprotected" Stroms!
Check all the easy and obvious: put the bike up on its centre stand and make sure it stands up properly. Some people don't know how to properly place the bike on its centre stand and repeatedly doing it wrong can (not always, but can) cause the bike to lean to the left or right when on the centre stand. Easy thing to check!
While the bike is still on its centre stand, eye the rear wheel alignment just to make sure it's good (takes a few seconds and with the DL is very easy to notice visually if the wheel alignment is bad).
Rotate the rear wheel and check for tooth wear on the rear sprocket. If he's willing to take off the front sprocket cover, he can check that for worn teeth too!
Obviously look at the general condition of the bike. At 10k miles it should be in fairly good nic (depending on whether or not it has been ridden during winter like mine has). The chain should be clean and have no dead links (checking for dead links is as easy as rotating the chain and lifting the slack from the underside of the chain. If you release it and it falls back neatly in line, then it's good. If it sticks or takes a moment to form back in line, then the chain is worn more than it should be at 10k miles!)
Do the standard checks (indicators, lights, brake lights). Test the front and rear brakes respectively. Test the horn (why not, eh?)
If it has engine bars and skid plate attached, make sure they don't "wobble" by grabbing them and giving them a gentle shake. Same with the side pannier rails.
Check the colour of the oil in the sight glass. At 10k miles it should still be fairly clear rather than tar black, assuming it has been serviced according to the schedule. It's a minor issue, of course, as an oil change is a 10 minute job and replacement oil filters are cheap enough.
Listen to the engine idling without a helmet on. If it's "sputtering" at all, this could indicate many things, one of which would be the need to replace the air filter. Again, that's a servicing issue.
You'll want to see a service history, of course.
Take a tyre pressure gauge with you and check the pressures. Also check the Tyres themselves for adequate tread and any bald spots.
Check the radiator casing (right-hand side of the bike's engine at the front, with the big water pipe running into it) to see if there are any paint chips/flecks peeling. This shouldn't be a deal breaker, but you'll want to either keep it covered with ACF50 or touch it up with Hammerite to prevent rusting on that cover!
Should point out that by 7,500 miles my DL650's water tank cover thingie was losing paint, but I'm now at 15k miles and there has been no further corrosion thanks to things like ACF50 and Scottoiler FS365.
I'd expect there to be some missing paint on the rear end of the swingarm. No matter how much TLC I gave my DL650, it still lost paint there (even before I rode through winter). Of course it's really easy to spray some black Hammerite on the bald spots to keep the problem from spreading futher!
I'd ask if the butterflies have been removed from the STVA, as this would make the take-offs much quicker (thus, if you aren't prepared, a little dangerous). If the seller doesn't know what the butterflies or STVA are, I'd say it's a safe bet that they haven't been removed!
Since you're a Strommer already, I assume you'll be going with him to check it out. You could always take a short test ride to compare it with the way your bike feels.
Check the front forks right at the top to see if they've been lowered at all (it'll be obvious, especially if you compare with your bike).
Check the top of the fork's inner tubes to look for rusting and/or fork oil lines which would indicate damaged/leaky fork seals. Again, it's not uncommon for the tops of the fork's inner tubes to get some rust on them, but generally this will only occur above the top point of travel (basically where the inner tubes never enter the outer tubes, thus are always exposed to air). Not a deal-breaker, but something to keep your eye on and possibly have sorted by a dealership or competant mechanic.
Check as much of the frame over as you can looking for any cracks in welds or other signs that the bike has previously been involved in an impact and subsequently "repaired". I say that because it's not that difficult for someone to replace the plastics and cowelings after a crash, and ignore any REAL damage on the frame itself. Obviously just eyeing it with all its clothes on won't be a sure-fire way of telling if it's had an accident, but if there are obvious cracks in welds etc. that you CAN see, odds are there's a lot worse you CAN'T see!
Check the rear ABS sensor cap (if the bike has ABS) to see if it has detached from its mount, or if the mount itself has a crack in it. It's certainly not a deal-breaker, but keep in mind that a replacement rear ABS sensor and cable is ~£150 from Suzuki, so if it is cracked/damage I'd try to reflect that in the offering price!
Check the front and rear brake fluid resovoires for discolouration of the brake fluid (and of course for good fluid levels). Certainly not a deal-breaker, but something you'll want to take care of ASAP. Same goes with the brake pads on the front and rear calipers. You should be able to visibly see some meat on the pads by looking at the point where the calipers surround the discs. If there's little-to-no meat on the pads, you'll want to replace them and I'd say reflect that in the price by knocking off £50 (if it's all pads), or £25 if it's just the rear!
Check the rear brake lever for "sticking" when pressed (or delayed return). This shows poor maintenance, but can be easily resolved by heavily lubricating the rear brake assemblies. Note that a squirt of WD40 isn't going to get it done! You'll need to use something heavier like GT85 or even FS365/ACF50 if it's really bad!
Similarly, check the front brake and clutch action to look for sticking or unusual return behaviours.
Test every key position in the ignition barrel to ensure that the key doesn't stick, and that the bike behaves properly. Borked ignition barrels are (it seems) fairly common on the Stroms, but I personally haven't had any issues. There again, I do spray the inside of my ignition barrel with WD40 every time I clean the bike!
Engage the side stand and slowly release it. It should readily spring back up quite quickly. If it sticks, this indiciates poor maintenance, and you'll need to adequately clean and lubricate the side stand mechanisms. I'd suggest in that case you clean and lubricate ALL lubrication points, especially the gear lever mechanisms right up to the clutch assembly under the front sprocket housing (which you'll likely also need to clean out thouroughly).
Why not take a paperclip, lift the saddle and put the bike into "Maintenance Mode" to read off any failure codes. It helps if you have a list of failure codes to reference so you can see what these mean (they're all listed and explained in the Service Manual). Ideally there should be absolutely no failure codes (00 should display).
Anyway, that's everything I can think of "off the top of my head". It's quite a list but, aside from the test ride itself, should only take about 15 minutes to get through at the most.
Hope it's not a lemon and he enjoys it
P.S.
If he's also in Ipwsich, I'd be happy to go along for the viewing and perform these checks myself if that's useful to him at all?