Hi Sharon and welcome
To clarify, you are trying to retrieve an email that you deleted from Gmail correct?
Please let me know.
If it was in Gmail Sharon we would have an option to recover it but in Facebook there is only the option if you archived it.
When via your computer within the Messages section of facebook, click on More and Archive and check for it there.
If it is not there it will not be possible to recover sorry as they have no undelete service for this.
If you have any problems, or would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service by clicking one of the stars at the top of the screen then submit, that would be greatly appreciated.
Yes if it is not in the archived folder then it is not possible, this I indicated just now.