As far as I know (this is from the top of my head and I’ll have to double check this at home) an animation can be used in a place if…
The animation is uploaded to the same group as the place belongs to.
The group owner of the group to which the place belongs has the animation in his/her own inventory.
The place is a personal place but the animations used are part of a group the place’s owner belongs to (and I assume certain permissions within the group need to be set?)
This is all from the top of my head though and I might be wrong, but this should at least help a little bit.
Animations uploaded to a group can only be used in games of that group. If you want to “transfer” animations, you need to re-upload them to the desired place (second group or your profile, depending on where it goes).
I think that’s how it should work. But I think its more flexible than that. In that some (but not all) of my group animations seem to work in non group places.