yes you dont own the messages which are on the other phone, however who does own them?
Any content that is on someone’s phone belongs to the owner of the phone. And what’s on your phone belongs to you. So the same content can belong to more than one person.
Look up Rabbeinu Gershom on the ban of reading someone else’s mail.
Some of what is found on the subject:
Reasons for the Ban
There are a number of reasons given for this ban:
We do not look at others’ correspondence so that we do not come to reveal gossip or a secret, as that would be rechilus (forbidden talebearing).2
<b>Reading someone else’s writings without permission is like borrowing something without permission, which is a form of theft.</b>
It is incompatible with the rabbinic teaching, “Don’t do unto others that which you do not want [to be done] to you.”
<b>May one who received a letter or email from an individual reveal to others what was written?</b>
One who received a private letter or email from an individual is prohibited from sharing it with others, unless he receives explicit permission from the sender. Accordingly, that which people are accustomed to forward private emails or messages to other acquaintances, may only be done if one has explicit permission from the sender.