What happens when I move apps to another organization?

Hi,

I’d like to move some apps (including a Postgres cluster) from my personal to another org (in the same account). As there isn’t much in the documentation about that process, I am a little hesitant just doing it. What can I expect? Will there be a longer down time? Do I need to move all apps at once (like can my apps from the personal org access the PG in the other org?)? Thank you.