...but related correspondence like extension offers etc continues to go to the original purchaser's email so you'll probably never get a chance to benefit from them.
OP, you should get a paper copy of the owners Refresh contract. It will have the contract number on it so if you want to renew it, thats what you will need. It is not transferable to your name, but is still in force no matter who owns the drone.
And if you want to confirm the remaining balance for the DJI Care policy, you can find that by entering the aircraft serial number on DJI's website here.