Is it permissible to wipe over the clothes worn by an employee at work, by analogy with wiping over socks, if he put them on while in a state of ritual purity (wudu')?

It is not permissible to wipe over clothes when performing ablution (wudu') instead of washing the hands. It is obligatory to wash the hands up to the elbows. One can roll up the sleeves or take the hands out from under the clothes if they are tight.

The Prophet, peace and blessings be upon him, did this during the Battle of Tabuk, where he took his hands out from under his jubbah (cloak) to wash them. If wiping over the outer clothes were permissible, the Prophet, peace and blessings be upon him, would have done it.

Rolling up the sleeves of a pullover or a suit to uncover the area to be washed is usually easy. If it is not possible, one must take off the pullover and wash the hands. There is no harm in the upper part of the body remaining uncovered, as a man's 'awrah (intimate parts) is between the navel and the knee.

It is obligatory to advise those who abandon prayer, as abandoning it is one of the major sins.