Start on the old phone
Go to Settings, choose Transfer cards, then Start transfer. ShowCards encrypts your wallet and shows a Transfer QR code. Leave it on screen.
Receive on the new phone
On the new phone open Settings, Transfer cards, then Receive cards, and point the camera at the QR code on the old phone. The cards come across encrypted; the transfer expires after 24 hours and is removed once it is done.
Choose how they are added
When the cards arrive you pick how to bring them in: Merge, skip duplicates adds only cards you do not have; Merge, add new labels and notes fills in extra details on cards you already have; Add everything imports them all, duplicates included; Replace my cards swaps your wallet for the incoming one.