My tranny started to not want to go into fourth. Then it didn't want to shift up at all.

The current theory is that when the radiator was replaced, two quarts of transmission fluid were left inside and never replaced. I have a transmission cooler installed . Does this still allow fluid into the radiator? More to the point, can I give the bill for the repairs tp the shop that did the radiator work?

Is there any chance of damage from the months of low fluid?