Is it obligatory to go to another mosque to pray in congregation if the congregational prayer was missed in the first mosque due to negligence, or due to thinking it was still ongoing and then realizing it had been missed?

If someone misses the congregational prayer in one mosque, it is recommended for him to move to another mosque to attain the reward of congregational prayer. However, this is not obligatory. What is obligatory is performing the prayer in congregation, whether it is in a mosque or elsewhere.