I was wondering if I was able to get an activity log between myself and a specific number? Just information between myself and this person?
You can get time/date information but not message content by looking in the account owner's MyVerizon account.
If you want message content, you need to look on your phone, online in your MyVerizon acct if you are using Verizon Message+ as your messaging platform or at a back up you have made of the messages.
