Praise be to Allah.
I put this question to our shaykh, ‘Abd ar-Rahman al-Barrak (may Allah preserve him) and he said:
[The government] that granted this assistance gave this amount to both of them to cover the expenses of both of them, because they are a married couple. Therefore they both own the money that is given to them to meet their needs as a married couple. Therefore neither of them has the right to take his own share to the exclusion of the other.
Based on that, they should spend on themselves as a couple from this money, then if any of it is left over, they may divide it equally between themselves. End quote.
And Allah knows best.