We consider the initial and progressive enlargements of a ltration (called the reference ltration) generated by a marked point process with a strictly positive random time. We assume Jacod's absolute continuity hypothesis, that is, the existence of a nonnegative conditional density for the random time with respect to the reference ltration. Then, starting with the predictable integral representation of a martingale in the initial enlargement of the reference ltration, we derive explicit expressions for the coecients which appear in the predictable integral representations for the optional projections of the martingale on the progressively enlarged ltration and on the reference ltration. We also provide similar results for the optional projection of a martingale (in the progressively enlarged ltration) on the reference ltration. This paper also extends the results obtained in our previous paper [14] in the Brownian motion setting to the case of absolute continuity hypothesis. * This research beneted from the support of ILB, Labex ANR 11-LABX-0019.