How does a latecomer complete the prayer with the congregants after he led them due to the imam's ablution being invalidated, while he himself was originally a latecomer?

The majority of scholars permit the Imam to appoint a latecomer (masbuq) as his successor. This is the relied-upon position of the four Madhhabs. However, it is preferable to appoint someone who is not a latecomer. The latecomer who is appointed as successor must observe the prayer of the Imam who appointed him, meaning he should sit and perform the prostrations of forgetfulness (sujud al-sahw) as the Imam did, and then complete his prayer. The congregants have the choice either to say the salām or to wait to say it with him (this is the view of the Shāfi'ī and Hanbalī Madhhabs). The Mālikīs said: He should signal to them to sit until he completes his prayer and they can say the salām with him. The Hanafīs said: The latecomer should appoint someone who caught the entire prayer to lead the people in salām.