Argent mobile
No. Upon recovery the wallet will be disabled on the original device. This is helpful if your phone gets stolen, as your wallet will be rendered inoperational on the lost device.
Argent X (browser extension)
You can use your wallets on multiple devices.
Important notes:
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The order of your accounts in Argent X will not transfer to the new device.
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You will need to re-authenticate with 2FA when setting up on a new device.