What should a person who made a vow do if they vowed to perform a prayer upon the fulfillment of a certain condition, and then a part of this condition was fulfilled, given that there is an opinion that physical vows cannot be fulfilled before the complete fulfillment of the condition? And should the person who made the vow strive to fulfill the remaining part of the condition that is within their power to discharge the vow?

A conditional vow (Nathr Mu'allaq bi Shart) does not become binding to fulfill unless the condition is met. If only part of the condition is met and not fully, then its fulfillment is not obligatory. Fulfilling the vow before the condition is met is permissible but not obligatory. The one who made the vow is not obligated to bring about the condition upon which he tied the vow, because "that without which an obligation cannot be fulfilled is not obligatory for the servant to do, by agreement of the Muslims."