Is it permissible to repeat the Fajr prayer with the intention of making it up (qadaa') during its prescribed time if one forgets one of its pillars?

There is no harm in re-performing the prayer within its time with the mistaken intention of making it up (qada'), and its re-performance is valid. For if one prays with the intention of performing it on time (ada'), but it becomes clear that the time has elapsed, it counts as a make-up prayer (qada'). And if one intends it as a make-up prayer (qada'), but it becomes clear that it was performed within its time, it counts as a prayer performed on time (ada'). The intention of performing it on time or making it up is not a condition for the prayer.