Does the traveler who moves between cities in the same country and stays in each for more than three days continue to offer the shortened prayer (Salat al-Qasr), or do they pray the full prayer (Salat al-Muqim) after the third day in each city?

The decisive factor in the ruling on shortening prayers (qasr) is the distance traveled, whether within the country or outside it. A traveler—to Syria or elsewhere—if he intends to reside for a period that interrupts his journey, must pray four rak'ahs from the moment he forms this intention. It is not permissible for him to shorten prayers for three days and then complete them thereafter.