Couple of thoughts.
First, I'd consider the history of real world maritime salvage law and why it is in place. Real world maritime salvage of a wreck usually yields a 10% to 25% prize claim of whatever is salvaged. That's 10%-25% of the value assigned to whatever was actually salvaged by a prize court... not the blue book mint, just out of the ship yard value. So if the wreck is badly damaged and barely running, its not going to be worth as much.
Maritime salvage laws came about to encourage people to risk their lives and property to salvage valuable goods. Since 10-25% of the value is paid out, that's 75-90% back to the owner. Much cheaper and cost effective than the cost of replacing all the goods in most cases.
Whether the Imperium has such salvage laws in your TU should likely be based on whether you decide the Imperium thinks its worth encouraging salvage of wrecks... or if they can afford to just write it off. Personally, I think they'd have some sort of salvage law to address just what happens to whatever is occasionally salvaged even if they don't want to actively encourage salvage (and I think they would personally, it just makes good economic sense). This takes care of the question of who a salvaged vessel (or cargo) belongs too and who is entitled to what. In the case you don't want much salvage going on, set the prize at only 5%... and its taxable income. So after taxes you get maybe 3% free and clear. If you are more comfortable with salvage, raise it to 10% as the standard with higher awards for specific wrecks (list of prize awards available at your nearest Imperial Navy base).
Under maritime salvage laws, ownership usually remains with the original owner. If we follow this model then no, the PCs couldn't just fly off with a salvaged Kininur... if they did, they're now pirates... yo-ho.. yo-ho. Maybe the PCs are fine painting it black, renaming it the Pearl and... :rofl: Otherwise, fly it to the nearest Navy base or depot and submit a claim to the prize court. After the Navy has had time to crawl over the salvaged ship and evaluate it (GM should take a few game sessions for this, figure out what was damaged or destroyed and deduct the value, then take off some more for whatever repairs would be needed to bring the ship back online OR just look at the ship as salvage... what would it be worth broken down for parts and scrap? Figure it up, PCs get 10% of that... possibly up to 25% for specific parts... like a black globe generator for example). After a few weeks, the prize court reports its findings and pays out their salvage fee.
If the ship were privately owned, then the owner has to come up with that salvage prize... which can get interesting if the owner is broke. The ship could be sold off and the PCs paid from the sale (getting a percentage of the sale price) or they might work out a deal with the owner of some sort... which could lead to adventure.
So taking the Kininur as an example. Out of the shipyard it is worth 1,663.63 MCr. Assuming battle damage destroyed or seriously damaged say 30% of the ships systems, we could knock that down to (1,663.63x70%) 1,164.541. If it would take another 10% to bring it back up to ready status, decuct another 166.363 MCr which leaves the salvage value down to 998.178 MCr of which the PCs get 10% of that for 99.8178 MCr... still a very hefty sum. Course taxes take off from that (due immediately of course) which could be another 20-30% easily so cut that down to 69.87246 MCr to be divded how many ways? Say 30 people (what, you took a prize crew out didn't you?) works out to 2.329 MCr per person.
If a PC coming into 2.329 MCr will wreck your campaign... well... maybe you're just a cheap ba&#^&# :rofl:
But that's just my 2 MCr on it
