Not a new suggestion, it's quite common but your exact idea is a bit different so here I am responding :S
A few issues:
1) So in a new account I can offer to move someones cutter, steal it and fly to Sag A* for a few weeks. When I come back the bounty is gone into a legacy fine. I sell the ship, pay the fine and profit?
Sounds a bit silly since my new account can be re-set at will so if I mess up I can just try again.
2) Oh and: Lets borrow a Corvette, go bounty hunting for millions of credits and then deliver it a touch damaged but I've made many times what I'd have been able to in a sidewinder.
3) Then there's: Here, move my ship, it has 3Ly range... Good luck.
Or no weapons or shields and lowest rated gear.
Or not enough power to use thrusters.
Solution imo:
If it were to be implemented then I'd vote for a 100% insurance option where the transferrer pays a set amount of credits based on ship value, ship type, jump range and distance. Say 1% or something like that. But pays no repair, fuel or insurance costs. Mission has a time limit, if not completed within the limit the ship self-destructs. No credits can be gained whilst transferring except the fee being paid, hardpoints do not deploy unless fired upon first.
Ranked so that the transporter can only transport certain values of ships so can't take a Corvette/Anaconda with a new account and earn 8mil per trip.
Covers costs for both sides, exploits and people trying to annoy others. Yes it means you can't steal ships but that can be developed later when adequate control methods get thought up. Missions quit before leaving the station don't reduce rank, missions quit afterwards do (hence avoiding the number 3 sub-issues).