Need to recover deleted text message without iCloud and iTunes backups

What you are trying to do is pretty much impossible if you don't have a backup.

I could easily examine my cellular carrier's records (AT&T) if I sent or received an SMS text message to learn the recipient's telephone number.

William R Rudloff wrote:

I called Sprint and they don't keep track of the SMS numbers ...

I did not realize that. As I say, AT&T does keep track. The SMS numbers actually appear on the detailed monthly statement, along with the date and time of the SMS transaction.

HHow would I go about getting the records from my carrier for deleted messages

i bought my sister an iPhone and have now upgraded to a newer model. Once I swapped her old one out to the new one I deleted her texts messages so I could use it for my daughter to listen to music. She now realized there were some texts mmessages she needs from her old phone that has now been erased. She didn't back her old phone up because it was only 8Gb and there wasn't any room to update or back up because of the memory issue. Is there a way to retrieve these messages without a backup? Maybe a safe app or a third party download software to computer. Thank you in advance kind of desperate here.... I feel awful but I thought she was done with the old phone.

There is no way to recover deleted texts, unless the person at the other end saved them.

The carrier will have a log of when they were sent or received, but not the contents.

I don't accept that she couldn't back it up; a backup takes no space on the phone itself. It could have been backed up to iTunes on a computer or to iCloud: About backups in iCloud and iTunes - Apple Support

As iCloud backup is almost automatic (you just have to turn it on) she may have a backup that she doesn't know about.