What is the meaning of "the Imam bears it on his behalf"? And is the Imam required to perform the prostration of forgetfulness if a worshipper speaks inadvertently during the Fajr congregational prayer, and should he prostrate if a long time elapses between the speech and the prostration?

The meaning of the Imam bearing the forgetfulness (sahw) of the follower (ma'mum) is that the follower is not prescribed to perform the prostration of forgetfulness because he is subordinate to his Imam, and the Imam also does not prostrate in this case; rather, the prostration of forgetfulness is waived due to the person being a follower. Al-Khiraqi said: "There is no prostration of forgetfulness upon the follower, unless his Imam forgets, in which case he prostrates with him."