Is it permissible to replace the Imam with another during the prayer, starting from the second rak'ah, due to the first Imam's inability to complete the prayer or recitation because of intense crying, and his fear of prolonging it for the traveling congregants, and what are the consequences if it is not permissible?

If an imam experiences an impediment that prevents him from completing his prayer, it is permissible for him to appoint one of the congregants to complete the prayer. This is the view of the majority of scholars, and the imam's inability to complete the prayer or perform one of its pillars is considered one of the valid excuses for appointing a successor.

Thus, if weeping overwhelms the imam and he is unable to complete the pillar of reciting Al-Fatiha, he may appoint a successor. However, if he has completed the recitation of Al-Fatiha and then is overcome by weeping while reciting additional verses, he should stop his recitation and bow for rukūʿ. In this case, it is not permissible for him to appoint a successor because he can complete the prayer by limiting himself to its pillars.

The imam should try to control himself as much as possible so as not to inconvenience the congregants or disturb them. If he is overcome by unintentional weeping, there is no harm in it.

Based on this, if the imam had already completed Al-Fatiha, then his appointment of a successor was an error, and he should not repeat such an action, although the prayer itself remains valid. However, if the weeping prevented him from reciting Al-Fatiha, then his appointment of a successor was correct and permissible.