Need help with syncing animations

Hello,

I am working on a character creator and I would like to apply the same animations I use for the playable character to the hairstyles since they use the same rig, I am using a singular animation controller with all parameters and transitions set and I would like to synch the animations between the playable character and an instantiated GameObject (the character's hairstyle) which is parented to the player.

My issue is that the animations are not synchronized and when playing the jump animation the hairstyle floats way above the player (i don't know if this is caused by a parenting issue between the hair model and player model because for the other animations it doesn't happen).

Is it possible to use a single animation controller for different objects? If yes what can I do to have both the player and an instantiated GameObject play the same animations at the same time?