"If that movie theater belonged to me, I would be happy."
Translation:Se tiu kinejo apartenus al mi, mi estus feliĉa.
"posedi" is to possess, to "posedigi" would be to cause someone to possess - to give or donate, perhaps.
If you want to make a passive (since usually cinemas are not things that possess other things), you need a passive participle such as "Se tiu kinejo estus posedita de me".
That feels clunky to me, though.