Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
If one enters the mosque after the prayer is finished, he may make the adhan and iqamah. If a person wishes, he may pray without making the adhan and iqamah.
In his famous work, Fiqh As-Sunnah, Sheikh Sayyid Sabiq, elaborates on the subject as follows:
The author of al-Mughni states, “If one enters the mosque after the prayer is finished, he may make the adhan and iqamah.
Ahmad’s practice, based on what al-Athram and Sa`eed ibn Mansur recorded from Anas, was to ask a person to make the adhan and iqamah, after which he would pray with (some people) in congregation.
If a person wishes, he may pray without making the adhan and iqamah. `Urwa says, “If you reach a mosque wherein the people have already prayed, you may base your prayer on their adhan and iqamah, as theirs are sufficient for those who come after them.”
This was the opinion of al-Hassan, ash-Sha`bi and an-Nakha`i. Al-Hassan, however, said, “I prefer that he makes the iqamah. If he makes the adhan, he should do so in a low voice and not aloud, for some people may consider it out of place.”
Almighty Allah knows best.