Is it permissible for one who is capable to take a shroud from the mosque, and is he obliged to return it later, and how should the person in charge of the mosque act if a capable person requests a shroud?

The disposal of the shroud is contingent upon the donor's condition. If the donor stipulated that it be used for the poor, then it is not permissible for a person of means to take it or to spend it on himself. If no such condition was stipulated, it is permissible for a person of means to take it or to spend it on himself. If the donor stipulated that its equivalent be returned, then it is permissible to spend it on condition that the equivalent is returned. However, if the shroud was purchased from charity funds, then it should only be spent on the poor and the needy.