Access

[pete_1762]

How do I access my messages from another phone?

[Sansan]

Voicemail or text messages?

If vm, just dial your phone number from the other phone and when your greeting plays, press the corresponding number (1) to listen to your messages.

If SMS, only option would be to move your SIM card (physical) only to the other phone and check your messages. 

If you don't have access to the original phone then consider them lost.

[slusagm]

You can't with PM.   PM only send you the message once and will delete it

But if you use RCS and iMessage, they have setting to sync across phones