Wearing a Khuff over Socks: Which to Wipe Over in Wudu?
Question

I wore the socks under my shoes after performing Wudu. Then I made Wudu and wiped on the shoes. If I take my shoes off, am I permitted to continue the wiping for the allowed period of time, wiping on my socks?
Praise be to Allah.If a person wears Khuff (leather socks) over socks , or Khuff over Khuff, to which of them does the ruling apply? That is subject to further discussion.  
Shaykh Muhammad ibn `Uthaymin (may Allah have mercy on him) said:  

If he puts on socks or Khuff then invalidates his Wudu , then he puts something else on before he does Wudu, then the ruling applies to the first one. This means if he wants to wipe over them after that, he must wipe over the first one, and it is not permissible for him to wipe over the upper layer.
If he puts on socks or Khuff , then loses his Wudu and wipes over them, then he puts something else on over them, then he may wipe over the second layer, according to the correct opinion.

It says in Al-Furu`: ‘It is permissible according to Malik.’ An-Nawawi (may Allah have mercy on him) said: ‘This appears to be more correct because he put them on when he was in a state of purity, and the suggestion of those who say that purity is not complete is not acceptable.’ 
If we accept that, then it is the beginning of the period during which he may wipe (over the Khuff or socks ), and in this case he may wipe over the first (layer) without a doubt. 

If he puts a Khuff over a Khuff or socks , and wipes over the top layer then takes it off, can he wipe over the lower layer for the remainder of the period? I have not seen anyone who explicitly stated this, but An-Nawawi narrated from Abu Al-`Abbas ibn Surayj, concerning a case where an overshoe is worn over the Khuff: they are like a single Khuff, of which the upper layer is visible and the lower layer is hidden. I say: based on that, it is permissible to wipe over the lower layer until the period for wiping over the upper layer ends, such as if the upper layer of the Khuff is scratched off, he may wipe over the lower layer.” (Fatawa At-Taharah by Shaykh Ibn `Uthaymin, p. 192) 

“The overshoe or galosh is a Khuff that is worn over the ordinary Khuff, especially in cold countries. What is meant by the upper and lower (or outer and inner) layers is if there is a Khuff of two layers, then the upper layer is called the outer and the lower layer is called the inner.” (Al-Sharh Al-Mumti`, 1/211) 
Thus it is clear that if a person wears Khuff over socks, then he takes off the upper or outer layer of the two, if he wipes over it, then his taking it off does not invalidate his wiping, and he may wipe over the lower or inner layer, in all the cases mentioned by Shaykh Ibn `Uthaymin (may Allah have mercy on him), until the end of the period for wiping over the Khuff or socks . 
And Allah knows best.