They'd have to take the details of the person who actually didn't pay their fare to do that, which they neglected to do. Hard cheese, TfL.
No evidence on the face of it that the OP's partner didn't pay the fare, and no evidence they contravened a bylaw in respect of barrier misuse. They used the barrier in a perfectly legitimate way, as many people do - by having someone else tap their device.
In what way did the OP's partner not use a ticket barrier in the correct manner? It's not forbidden nor is it unusual for someone else to hold your ticket, or pay on your behalf. This bylaw criminalises people who jump the barrier, force the gates, crawl under them, or try to game them. There is no evidence at all the OP's partner did this at all - they passed through normally, the fare having been paid for them by the mother tapping her own card. They have paid their fare and showed a valid ticket (the mother's validated card), and used the barrier correctly.
It's actually the mother they want to pursue, for (allegedly) pushing the barriers and, having got through to the other side *second*, it was actually her who hadn't paid her fare!
This notwithstanding, a lot rests on what was said to the inspector at the time, especially if the partner made a straight up admission they didn't pay their fare (because perhaps at the time they asserted the tap was for the mother's fare, and the mother presented her card as evidence the mother had paid her fare), or similar. It is very important the OP gets a handle on what was said, exactly, by whom, as it will have been recorded either on bodycam or on contemporaneous notes by the inspector.
