Performing Wudu' without washing an injured spot then after starting Salah one remembers that they have not performed Tayammum

Q: A person performed Wudu’ (ablution), and because of a wound in his hand that should not be exposed to water, he performed Tayammum (dry ablution with clean earth) for not washing that area. It happened that he once forgot to perform Tayamum due to the wounded area, but during Salah (Prayer) he remembered, so he performed Tayammum without interrupting the Salah and continued praying. What is the ruling on this Salah? Is it valid or not?

A: All praise be to Allah Alone, and peace and blessings be upon the Messenger of Allah, his family and Companions. To proceed: If one of the body parts required to be washed in Wudu’ sustains a wound that must not be washed or wiped over with water, as this may worsen the wound or slow the healing, the person should perform Tayammum. If they perform Wudu’ and leave the place of the wound, then begin to offer Salah, and remember during Salah that they have not performed Tayammum, they should perform it and restart the Salah, as the part offered before Tayammum is invalid, including Takbirat-ul-Ihram (saying: "Allahu Akbar [Allah is the Greatest]" upon starting Prayer). Accordingly, the commencement of their Salah itself is originally invalid, as Taharah (ritual purification) is a prerequisite for the validity of Salah.Leaving one of the body parts required to be washed during Wudu’ or even an area of it unwashed invalidates Wudu’. When the Prophet (peace be upon him) saw a man on whose foot there was a shiny spot as tiny as a coin, which water has not reached, he (peace be upon him) ordered him to repeat Wudu’. (Part No. 5; Page No. 358) When washing and wiping become impossible, as in the case of the questioner, Tayammum should be performed, for Allah (Exalted be He) says: And if you are ill, or on a journey, or one of you comes after answering the call of nature, or you have been in contact with women (by sexual relations) and you find no water, perform Tayammum with clean earth Another piece of evidence is the story of the man wounded in his head, related by Abu Dawud on the authority of Jabir, concerning whom the Prophet (peace be upon him) said: It would have been sufficient for him to perform Tayammum, wrap or tighten (Musa doubted the exact wording) a piece of cloth around his wound, wipe over it, and wash the rest of his body. Finally, in case the questioner did not repeat that Salah, he should repeat it.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.