Sorry to see that it is the kind of issue that leads to trapped mantises in molts.
It is at such a strange angle she will likely have problems pulling her arm free. Many keepers will leave their mantis be in such cases, and hope for the best. Personally any I left be typically die from such deformities causing them to become trapped in a molt (which leads to death from them suffocating in the molting process).
As the arm is a extreme case I am listing the only methods I know that can help her. The methods are controversial to many, however, they can in fact save your mantis from dying. Use which ever method you prefer, as I can understand any decision as it can be difficult to make (and especially do).
There are two ways to prevent her death by molting problems. The first is to let her be and watch her closely for her molting. When she molts and the arm does become trapped you will have to use sharp scissors and cut the old exoskeleton to free her; however, as this is a arm, it is one of the first things pulled free in molts so there may not be enough room to cut the exoskeleton.
If it happens that you can not cut the old exoskeleton and she is trapped, the only alternative is to cut off her arm, amputating it as close to her body as possible. That could save her life, but having her arm removed during a molt may likely cause her to fall and lead to further problems (or her death). Also if you have to remove her entire arm, it will not regrow, at best she will likely develop a small stump arm.
The second option is to cut off the arm now, at her "elbow" (leaving part of her arm intact, removing just the bent part) so it has a chance to regrow in the few remaining molts before adulthood. The best way is to place the scissors on the correct location slowly, then ensuring it is placed properly do the cut in one single forceful manner to cause as little pain/damage as possible in this situation.
It sounds cruel but I've been forced to do it as well, and is the safest method to ensure she survives. I say safest as she will not become stuck in a molt and you are unable to help (as they can molt anytime typically early morning or early evenings (sunrise or sunset)), it has time to heal up a bit before molting, there is no worry of knocking her loose during the molt trying to cut it free, and such.
The cut arm will quit bleeding and develop a scab, and I recommend you put honey on the cut limb as it is a natural antiseptic as soon as you can after cutting it. She will heal up and adjust to having just one arm to catch prey in time - but likely is use to that now already as she can not use her arm. In the meantime you can feed her using tweezers until she figures out how to catch her own prey. In a few molts her arm should regrow enough to return to a usable arm, although it will never be the same size or appearance.
I wish you both the best, and hope she can pull it free on her own, but sadly I don't think that is possible. If you do amputate the arm she will return to her normal behavior/tameness within a few days to a week at most - once it heals up. Even if the arm does not regrow she should live a long happy life, as I had a male Ghost that only had one arm his entire life. His name was Bandit and was able to catch his own flies and crickets just with one arm, you can see photos of him in
my thread here.
