Can virtual extensions be transferred to other mailboxes (phsical mailboxes) instead of their own?

Example: Can virtual extension 350 be transferred to mailbox 102 instead of mailbox 350; if busy or no Answer?

You can do it in voicemail. You would need to create a voicemail x.350, then on the "Transfer?" setting, make it "Yes-->102."

Or you could make 350 a Transaction box that "belongs" to x.102, and leaves its messages there.

Do I need Cossesion to make 350 a Transaction box to x.102? Or could this be done from admin's telephone. If so what memory program sets that?

Yes, CO Sessions is needed to create a T-Box.