About Hair Animation I'm sorry if this question  already exists but I couldn't find it.

I know that there is an option for modifiers to extend the animation to more than 250 frames, but I cant find this option for the hair, so when making a video that is more than 250 the character keep moving but the hair stop moving.

How can I extend the hair animation to more than 250 frames?
You have to bake the hair dynamics. Sometimes the Blender bakes something automatically, sometimes not. The surething is the Bake button.