Without the phone the only way would be to sign in to with that phone number's MyVerizon credentials into the Verizon Messages app on another device that was previously setup to sync to.
It's possible without having the phone to look through, but you have to have the userid/password for the line in question. If you are attempting to do this without the knowledge of the person who actually uses the line, it is not likely to happen.
You could log into the MyVerizon account of the line in question on a computer or add the app to a tablet. Either way, you would need to have the password for the line inquestion.
We certainly want you to have access to these messages. You would not be able to see another number's messages from your device. If you've set an online profile for your MyVerizon, you can view, edit, and text from the desired phone number. You must have access to the phone to register for online access, though.
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