Hi there
I’d be happy to help with your voicemail concerns!
You would be able to perform a backup of the first phone without losing any information on that device. To do so, connect the device to iTunes and choose File > Devices > Backup in iTunes to begin. Once completed, try connecting the 2nd phone and choose Restore from Backup. Choose the backup that we just created and it will copy everything onto the 2nd phone.
If the voicemail messages are not present on either device, I’m afraid there would not be a way to recover those messages.
I hope this helps!
Charise