An Android app that forwards incoming messages to email or another number.
On iOS you don’t need a third-party app. The built-in Shortcuts app has an Automation feature that can forward any incoming message to your email automatically.
Open the Shortcuts app, go to the Automation tab, and tap New Automation. Choose Message as the trigger.
iOS requires at least one filter to activate the automation. To catch every incoming message:
A single space matches virtually all real messages, so this effectively forwards everything without needing to enumerate senders or keywords.

Tap Next, then add the Send Email action. Configure it:
Auto-Relay
Every incoming message triggers the automation and sends an email with the subject Auto-Relay.
Now you can leave your phone in the closet — no more picking it up just to check a code.