When is Tayammum valid, and is the prayer of one who performs Tayammum valid in the presence of water, under the pretext of lack of time?

It is not permissible to perform tayammum (dry ablution) when water is available and one is able to use it. What these sisters mentioned about being busy with work is not an acceptable excuse. Wudu (ablution) does not take a long time, and if it is estimated to do so, then they must delay the prayer so that its time does not expire; otherwise, it is not permissible to remain in this work.

They must repent to Allah and make up for the prayers they performed with tayammum while ablution was possible, because those prayers are invalid.

Tayammum is only valid when water is unavailable or one is unable to use it due to illness or similar reasons. Using tayammum when water is available is a great laxity and an ugly reprehensible act, and the prayer in such a case would be invalid due to the absence of one of its conditions.