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Hi there and welcome
No sorry, not deleted logs, you can get the logs, but once they are deleted they are gone.
Even backups will not backup the actual log for this sorry
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This is possible, but you need to use a program which is not free, called wondershare
This you download here
Onto your computer
Once installed you connect your phone to your computer and allow it to scan the phone
Once done, if any text messages can be retrieve, this program will retrieve it.