Is it obligatory to leave a mosque that contains a grave, or is it permissible to pray in it, and is it obligatory to interrupt the prayer of someone who has begun a supererogatory (Sunnah) prayer inside such a mosque?

If the grave is inside the mosque and not outside it, then prayer in it is invalid, due to the prohibition of the Messenger of Allah, Allah’s peace and blessings be upon him, and his curse upon those who take graves as mosques. So, if the grave is inside the mosque, it is not permissible for you to pray in it, and it is invalid. If someone begins to pray in it without knowing about the presence of the grave, they should be alerted and informed of the grave’s presence, without being ordered to leave the prayer.