He became Muslim at the time of prayer; should he make up what came before it?

He does not have to make up what came before it, because
Allaah says (interpretation of the meaning): 

“Say to those who have disbelieved, if they cease (from
disbelief), their past will be forgiven”

[al-Anfaal 8:38]. 

i.e., if they give up their kufr and become Muslim, then
Allaah will forgive them their previous sins, whether these were sins of
neglecting obligatory duties or doing haraam acts. But he must offer the
prayer at the time of which he became Muslim, if there remained enough time
to do one rak’ah or more, because the Prophet (peace and blessings of
Allaah be upon him) said: “Whoever catches up with a rak’ah of the prayer
has caught up with the prayer.” 

As for the prayers that came before, he does not have to make
them up, such as if he became Muslim after ‘Asr, he has to make up ‘Asr, but
he does not have to make up Zuhr, because the time for it had ended. End
quote. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him).