Answered by Shaykh Amjad Rasheed
Does performing ghusl alleviate the need for wudu?
Case 1: Merely Recommended Ghusl
If the ghusl is merely recommended, such as the Friday bath, it does not count as wudu, because performing wudu for prayer is obligatory while the Friday bath is recommended and the recommended does not alleviate the need for the obligatory.
Case 2: Obligatory Ghusl
As for if the ghusl is obligatory, such as bathing due to post-sexual impurity (Ar. janaba) or menstruation, it alleviates the need for wudu on the condition that nothing invalidate the wudu during it, such as touching the private parts or something exiting them. So if one wants to suffice oneself with an obligatory ghusl in place of wudu, one first washes the private parts with the intention of lifting ritual impurity from them and then intends to lift ritual impurity from the rest of one’s body. This way, one doesn’t need to touch the private parts after the [m: second] intention.
Amjad Rasheed
(Translated by Moustafa Elqabbany)