Is there a specific period after the father's death during which the son should not propose?

There is no specified period in Islamic law between a man's death and his son's engagement. However, customs should be observed without exaggeration. If haste harms the family's feelings, then one should wait until they accept, while avoiding excessive delays that could reach the level of innovations (bid'ah). The Permanent Committee has issued a fatwa (definition) stating that setting a period for a man to marry after his wife's death is a pre-Islamic custom (Jahiliyya tradition) that has no basis in Islamic law, and it is not permissible to ostracize someone who marries immediately.