What is the authenticity of the hadith: “There is no wudu for one who does not mention the name of Allah”?

Question:
What is the ruling on saying the name of Allah before wudu, and if a person does not say it, what is the ruling on his wudu? May Allah reward you with good.

Answer:
In the name of Allah, praise is to Allah, and blessings and peace be upon the Messenger of Allah, and upon his family and companions and those who follow his guidance. As for what follows:
Saying the name of Allah during wudu is a recommended practice (sunnah) according to the majority (the majority of scholars), and some scholars held that it is obligatory along with the intention. A believer should not leave it out. If he forgets or is unaware, he owes nothing, and his wudu is valid.
As for if he intentionally leaves it out while knowing the legal ruling, he should repeat the wudu as a precaution and to avoid the disagreement; because it was reported from him (peace and blessings be upon him) that he said: .
This hadith came through various chains, and a group of scholars ruled that it is not established and that it is weak. Al-Hafiz Ibn Kathir (may Allah have mercy on him) said that it is good due to the multiplicity of its chains, and that this falls under the category of good for other reasons. A believer should strive to say the name of Allah at the beginning of wudu, and likewise the believing woman; if they forget that or are unaware of it, there is no blame on them.