Is it permissible for worshipers to pray in the first row to the right of the Imam if the mosque is full?

If the question is about the congregants standing to the right of the Imam during extreme crowdedness, then there is no harm in that. Those standing next to him are not considered the first row, because the first row is the first row directly behind the Imam. However, if the question is about worshippers standing in the first row, then it is among the best deeds, and the right sides of the rows are better than their left sides. Whoever strives for good and desires it despite severe crowdedness will be thanked and rewarded.