Praise be to Allah.
We put this question to our shaykh, ‘Abd ar-Rahman al-Barrak (may Allah, may He be exalted, preserve him), and he replied:
If he has nearly finished his prayer and a slight delay will not matter, he should complete his prayer quickly and open the door. But if he has just started to pray, and any delay in opening the door could affect his job, then it is permissible for him to interrupt his prayer and open the door, as it is a case of necessity.
And Allah knows best.
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