It is not really possible to answer “yes” or “no” in a global way as it is fact dependent but if it is the same case with the same attorney and funds remain available on the prior allowed, you can use these remaining funds on remand. If the motion becomes exhausted you’d need to seek additional funds.
If the attorney type changes to a privately retained or pro bono (vice CPCS employed or appointed) then the new attorney will be required to obtain a new motion for funds.
Appeals are considered new cases; a motion for funds from the initial trial may not be used for an appeal. New motions are required for appeals.