How does one make up missed prayers for someone who missed one or more rak'ahs?

The Prophet, peace and blessings be upon him, clarified what a latecomer (masbuq) should do if they miss part of the prayer. He commanded them to follow the Imam and complete what they missed after the Imam’s salutation. The wording for completing the prayer varied between "fa'atimmu" (so complete) and "faqdū" (so make up), and the preponderant opinion is that what the latecomer catches is the beginning of their prayer. If someone misses one rak'ah with the Imam, they make it up after his salutation without vocalization, and according to the majority of scholars, they recite a surah after Al-Fatiha. If someone misses two rak'ahs, they make them up without vocalization, with a difference of opinion regarding the recitation of a surah. If someone misses three rak'ahs, they make them up in their known form, and if someone misses all four, they perform them in their known form. The preponderant opinion is that one is not considered to have caught the congregational prayer if they miss all the rak'ahs, although they may attain its virtue through their intention.