If a worshipper catches one rak'ah of Fajr prayer with the imam, and is delayed in reciting, should he complete the tashahhud or stand up to complete the prayer? And is it sufficient to say: "O Allah, bless Muhammad and the family of Muhammad" instead of the complete Ibrahimiyah prayer formula if the imam says the taslim before he completes it?

The latecomer (masbuq) must stand up to complete his prayer immediately upon the imam's salutation, even if he has not completed the tashahhud; because the tashahhud here is subordinate to the imam. So, when the imam says the salam, the latecomer must stand up, whether or not he has completed the tashahhud and the salutation upon the Prophet (peace be upon him). If the latecomer remains seated after the imam's salutation and prolongs his sitting, knowing that this invalidates his prayer, his prayer becomes void. However, if he was forgetful (sahiyan), his prayer is not void, and he should perform the prostration of forgetfulness (sujud al-sahw).