Well, now that it’s been captured, it should be easier to handle, anonymous. Simply take your new mimikyu to either an adoption center (shelter, pokémon center, breeding center, etc.) or create a listing on the Global Trade Station for it. The latter is perhaps preferable, as you’ll be able to connect with other verified trainers around the world and thus have better chances of finding a caring home for this mimikyu.
Best of luck, anonymous!