[It is permissible to perform ablution in one mosque and pray in another]

The answer, and Allah is the Grantor of success, is that there is nothing wrong with that, as it appears to me, because ablution is an independent act of worship, based on the words of Allah the Most High: {Indeed, Allah loves those who are constantly repentant and loves those who purify themselves.} [Al-Baqarah: 222], and the words of the Prophet (peace and blessings of Allah be upon him): “Ablution is half of faith.” Perhaps the reason for the questioner to ask this question is that the one who placed the water in the mosque only intended it for the worshippers in that mosque, so the one who performs ablution and then prays in another mosque has used the water for a purpose other than that for which it was placed, and that is not permissible. We say in this regard: Ablution is an independent act of worship, as we have mentioned, so the one who uses the water placed in a specific mosque for ablution and to remove major ritual impurity is not transgressing the purpose for which the one who placed it, because the one who placed it only placed it for that purpose.

What is impermissible is using water for purposes other than its intended purpose, such as draining homes or irrigating farms.
However, if the water is scarce, such that it is usually sufficient only for those praying in that mosque, then no one else should come there for ritual ablution or ritual washing. However, if they come for ritual ablution and prayer, they have a right to that water, since the one who placed the water in that mosque intends to revitalize it.

From the fruits of knowledge and wisdom by the eminent scholar, Mr. Muhammad Abdullah Awad, may God protect him