Is it permissible for a latecomer, upon standing to make up what he missed of the congregational prayer, to interrupt his prayer in order to join another congregation being established before him, and pray a complete prayer with them?

The jurists have agreed on the impermissibility of interrupting an obligatory act of worship once it has been commenced, without a legitimate شرعي (Shari'i) excuse. This is based on the Almighty's saying: "O you who have believed, obey Allah and obey the Messenger and do not invalidate your deeds" (Quran 47:33). The presence of another congregation for prayer is not a legitimate excuse for interrupting it.