My mom is coming into DFW today from LGW on BA 2193. It was originally scheduled to arrive at DFW at 1407 CST, but it left Gatwick an hour late and is now due to arrive at 1523. She is scheduled to connect on AA 477 scheduled to depart at 1605. What are the chance of clearing immigration, customs and making the 1605 to PHX--slim to none?

I checked out the next AA flight--it's sold out also
What are the chances of BA endorsing her ticket to an HP flight if the delay was mechanically related rather than mother nature? In case she misses her AA flight there is an 1805 HP departure to PHX that has a few seats left.
Sidenote, my mom has no elite status on AA/One World.
Thanks in advance!
Ian