Is a sum of money designated for 'Umrah, left by a deceased wife, to be distributed among the legal heirs, or is the husband entitled to keep it to perform 'Umrah on her behalf after his own 'Umrah?

The mentioned amount is an inheritance from your wife, and it must be distributed among the heirs according to Islamic law, unless the wife had not performed the obligatory Umrah while she was able to, in which case the Umrah should be performed on her behalf from her own money. If she had willed that, then the will should be executed within the limits of one-third of her money.

You do not have the right to take the amount without the other heirs, unless it is for performing Umrah on her behalf, provided that the other heirs give their permission.

There is no text mentioning the virtue of Umrah in Rajab, rather the virtue of Umrah in Ramadan was mentioned in the Prophet's (peace be upon him) saying: "Umrah in Ramadan is equivalent to Hajj with me."