Transfer ownership of OR copy a client's record from one TextUp phone to another

When handing off a client to a colleague, I would like the ability to also hand off the client's record in TextUp.

MODERATOR: when transferring ownership from one TextUp phone to another, how would phone numbers work? That is, if a client calls the original TextUp phone number, should those calls also be routed over the TextUp phone that now owns this contact?

MODERATOR: or maybe instead copying the contents of a client's record is enough?