Is it permissible for the chairman of the mosque’s board of directors to use the mosque’s refrigerator to store his personal belongings, under the pretext that there is no space in his home refrigerator, or are the mosque’s possessions an endowment that may not be exploited in this manner?

The mosque's board of directors oversees the endowment (waqf) and is responsible for its maintenance. It is permissible for them to benefit from the endowment in ways that do not harm it, such as placing items in the refrigerator when needed, by analogy with what was reported in the Hadith concerning Umar's (may Allah be pleased with him) endowment.