Following up on the one who prayed the obligatory prayer, then went to a mosque and caught two units of prayer with the congregation: is he required to complete the prayer, or is it permissible for him to be content with two units and conclude the prayer?
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The Shaykh : Sahih al-Bukhari 635.
As for the case where he fears missing the thing for which he came, such as one who came to pray over a funeral and caught two units of prayer with the imam, in this case he concludes the prayer with the imam, because it is permissible to perform a voluntary prayer of two units. He only attended for the funeral prayer, and the funeral prayer is better for him than completing the prayer, because the funeral prayer is a collective obligation. Thus, he shares in the obligation with the other worshippers, and the obligatory is better than the voluntary. So he concludes the prayer with the imam in order to catch the funeral prayer.
and pray whatever you get (with the people) and complete the rest which you have missed
ما أدركتم فصلوا وما فاتكم فأتمواAs for the case where he fears missing the thing for which he came, such as one who came to pray over a funeral and caught two units of prayer with the imam, in this case he concludes the prayer with the imam, because it is permissible to perform a voluntary prayer of two units. He only attended for the funeral prayer, and the funeral prayer is better for him than completing the prayer, because the funeral prayer is a collective obligation. Thus, he shares in the obligation with the other worshippers, and the obligatory is better than the voluntary. So he concludes the prayer with the imam in order to catch the funeral prayer.