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Hello. Thanks for the question.
To be completely honest with you, that is your cat. You feed him, you let him in the house and you care for him- he's just a mostly outdoor cat.
I would keep the cat indoors for the first week or two initially. You can then let him out when supervised. Over a few months, you can start letting him out more and more. He'll know where the food is and he'll come back.
Let me know if you have any other questions.