He put on short socks that come below the ankles over long socks; is it valid to wipe over them?

In order for it to be permissible to wipe over the socks, it is stipulated that they must cover the place that is to be washed when doing wudu

In order for it to be permissible to wipe over the khuffs or socks, they must cover the place that is to be washed when doing wudu, which is the entire foot, from the tips of the toes up to the ankles. Please see the answer to question no. 192736 .

If someone puts on khuffs over khuffs, or socks over socks, before invalidating his wudu, and both pairs are intact, it is permissible to wipe over either of them.

But if they both have holes in them, or both are short, it is not permissible to wipe over either of them, according to the view that it is not permissible to wipe over the one that has holes, which is the view of the majority.

If one of them is short or has holes, it is valid to wipe over the outer one in all cases. In other words, whether it is the long sock or the short sock.

It is valid to wipe over the inner sock if it is intact, by inserting one’s hand under the outer sock and wiping the inner sock.

It says in Matalib Uli an-Nuha (1/132): If someone who is wearing a khuff puts another khuff over it, so long as his wudu is still valid, even if one of them has a hole in it, it is valid to wipe over the outer khuff in all cases, and to wipe over the inner one if it is the one that fulfils the condition of being intact. It is not valid to wipe over them if both of them have holes, even if, together, they cover the foot.

If both of them are intact, then it is valid to wipe over whichever of them he wishes.

If he wants to wipe over the inner one, he may put his hand under the outer one and wipe the inner one.

If the one who is wearing two khuffs takes off one of them, then he must take off the other one and repeat wudu. End quote.

In Hashiyat Ibn Qayid ‘ala al-Muntaha (1/63), it says: If he puts another khuff over it … – That includes four scenarios: either they are both intact, or they both have holes, or the outer one is intact and the inner one has holes, or vice versa.

In the first scenario, it is valid to wipe over either of them. In the second scenario, it is not valid to wipe over either of them, even if, together, they cover the foot. In the third scenario, it is valid to wipe over the outer one only. In the fourth scenario, it is valid to wipe over whichever of them he wishes. End quote.

Ruling on wiping over the socks when there is another pair of socks under them

What you have described is the fourth scenario, so it is valid to wipe over the outer socks and it is valid to wipe over the inner socks by putting your hand under the outer one and wiping the inner one.

If you take off the outer sock, you must also take off the inner sock.

Wearing a short sock over a long sock is like wearing a sandal over the khuff. At-Tirmidhi (99), an-Nasa’i (125), Abu Dawud (159) and Ibn Majah (559) narrated that al-Mughirah ibn Shu‘bah said:

The Prophet (blessings and peace of Allah be upon him) did wudu and wiped over his stockings and sandals. This hadith was classed as sahih by al-Albani in Sahih Abi Dawud.

Shaykh Muhammad ibn Ibrahim said: It is valid to wipe over shoes that do not cover the required area, provided that there are thick socks under them that do cover the required area, on condition that they are both put on together, or that the wearer put the shoes on before he invalidated his wudu, and on condition that he only takes them off together, because the Prophet (blessings and peace of Allah be upon him) wiped over his khuffs and sandals [when he wore them together].

He may also wipe over the sock only, but in this case it is not stipulated that he should have put them both on together and the like, or that he must take them both off together."(Fatawa ash-Shaykh Muhammad ibn Ibrahim 2/68).

Conclusion: It is permissible to wipe over short socks that are worn over long socks, and to take them off together.

And Allah knows best.