Wallet can be moved from one phone to another without closing payment channels and this can be achieved in two different ways:
The first option is to make a full wallet snapshot in
Settings -> Use wallet migration tool, then transfer a snapshot file to a new phone, then install a fresh copy of BLW there and use
Restore wallet -> Use migration file. Do not forget to remove a snapshot file after doing this as file is not encrypted.
The second option is to restore an on-chain wallet on a new phone by using a mnemonic phrase which would trigger an automatic fetching of latest channel backups from GDrive. Before proceeding with this please make sure GDrive backup is enabled in wallet settings.
It is safe to have multiple copies of the same on-chain wallet restored from the same mnemonic phrase running on different phones but only one of those phones should have open channels. Otherwise there is a risk of those channels being force-closed by remote peers due to synchronization issues.
Next: Recovering lost balance