The Typhoon H uses 4S batteries (as in series) not 4P (as in parallel). What charger are you using? If the battery will not fit the charger it will not fit the Typhoon H either.
Edit: I need to amend my post. The 4P battery you are referring to is for the Typhoon H Plus and the H480 and is a LiHV (lithium polymer High Voltage) battery. To my knowledge it is usable in the H480, but the pins are slightly different for the balance leads and won’t work in the OEM charger for the H480. The OEM charger for the H480 is for a standard LiPo and would not fully charge the LiHV pack.
When you stated a 4P battery I was thinking of it as a 1S4P battery that would be only be a 3.7V battery pack.