He entered the mosque and prayed on his own then left before the prayer in congregation
Question

A person entered the mosque at the time of the adhaan for ‘Asr, then he prayed and did not wait for the iqaamah (call immediately preceding the prayer) to be given, because he had something to do. Is that permissible or is it not permissible to pray until the iqaamah for the prayer is given?.
Praise be to Allah.The Muslim should pray in congregation in the mosque if he is able to do so. 
This has been discussed with the evidence in the answer to question no. 8918  
If he has an excuse, then there is nothing wrong with him praying before the congregational prayer on his own, then leaving. 
One excuse is if he remembers that he has some property that he fears may be stolen, or he has a family member who is sick and he has to stay with him, or he has an appointment and will be adversely affected by not attending it, and other excuses that make it permissible to waive the duty to attend prayer in congregation. 
And Allah knows best.