A Team-on-Team Tussle!

When Team Rocket see Ash and Kiawe demonstrating Z-moves, they plot to find Z-crystals for themselves. While searching, Team Rocket run into Team Skull. Both gangs spot a Darkinium Z-crystal embedded in a large rock. Will they be able to work together to get through the infestation of Rattata and Raticate from earlier that are between them and the Z-crystal? If they can, how long will this alliance last? If they can't, who will get the Z-crystal first and will they be able to use it?