Would appreciate if you could advise on the following question. Can my mother-in-law be accompanied by her nephew (sister's son) as her Mahram on her Hajj pilgrimage?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

It is permissible for a woman to travel while being accompanied by her nephew since he is among the unmarriageable persons (i.e. he is a Mahram to her) and she is his maternal aunt.

Allah Says (what means): {Prohibited to you [for marriage] are your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters, your [milk] mothers who nursed you, your sisters through nursing, your wives' mothers, and your step-daughters under your guardianship [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you. And [also prohibited are] the wives of your sons who are from your [own] loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful.} [Quran 4: 23]

It does not matter whether the journey is for Hajj or for other purposes.

Allah knows best.