Praise be to Allah.
Formal mourning, which involves refraining from adorning oneself or wearing perfume for a specific length of time, is something that is required only of women, not men. So if a woman’s husband dies, she must observe ‘iddah and a period of formal mourning.
Ibn Qudaamah (may Allah have mercy on him) said: The wife whose husband has died must avoid wearing perfume and adorning herself… This is called ihdaad (formal mourning), and we do not know of any difference of opinion among the scholars concerning the fact that this is obligatory for the woman whose husband has died.
End quote from al-Mughni (8/125).
It says in Fataawa al-Lajnah ad-Daa’imah (20/479): The woman whose husband has died must observe ‘iddah and a period of formal mourning. End quote.
In the case of a man, however, he is not required to observe a period of formal mourning, according to scholarly consensus.
It says in al-Mawsoo‘ah al-Fiqhiyyah (2/105): The scholars are unanimously agreed that no period of formal mourning is required of a man. End quote.
It says in Fataawa al-Lajnah ad-Daa’imah (19/156):
In the region where we live, there is a custom whereby if a woman dies, the husband does not marry again until six months or more after that. If you ask them why they do that, they say that it is out of respect for the wife. It so happened that someone got married one week after his wife died, and the people did not go to his wedding, or even greet him with salaam. Is getting married again, even one day after the death of one’s wife, permissible according to Islamic teachings or not?
Answer: This is a jaahili custom for which there is no basis in Islamic teachings. Hence you should advise them to ignore this custom and pay no attention to it. It is not permissible to shun someone who gets married straight after his wife dies, because this is shunning for which there is no basis in Islamic teachings. End quote.
And Allah knows best.