If he puts on the khuffs at Fajr, can he wipe over them until the following Fajr?

Firstly:

The saheeh Sunnah indicates that for one who is not travelling, the period during which he may wipe over the khuffs is one day and one night, and for the one who is travelling it is three days and three nights. Muslim (276) narrated that ‘Ali ibn Abi Taalib (may Allah be pleased with him) was asked about that and he said: The Messenger of Allah (blessings and peace of Allah be upon him) set a limit of three days and nights for the traveller, and one day and night for one who is not travelling.

At-Tirmidhi (95), Abu Dawood (157) and Ibn Maajah (553) narrated from Khuzaymah ibn Thaabit (may Allah be pleased with him) from the Prophet (blessings and peace of Allah be upon him) that he was asked about wiping over the khuffs, and he said: “For one who is travelling, three [days], and for one who is not travelling, one day.” Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.

Secondly:

The scholarly view that is most likely to be correct is that the time for wiping over the khuffs begins from the first time one wipes over them after invalidating wudoo’, not from the time when one puts them on. So if someone does wudoo’  for Fajr prayer and puts on his khuffs, then he invalidates his wudoo’ at nine o’clock in the morning and does not do wudoo’, then he does wudoo’ at twelve o’clock, then the time for wiping over the khuffs begins at twelve o’clock and lasts for one day and one night, i.e., twenty-four hours.

An-Nawawi (may Allah have mercy on him) said: al-Awzaa‘i and Abu Thawr said: The time for wiping over the khuffs begins from the first time one wipes over them after invalidating wudoo’. This was narrated from Ahmad and Dawood, and it is the favoured view and the strongest in terms of evidence. This view was favoured by Ibn al-Mundhir, and something similar was narrated from ‘Umar ibn al-Khattaab (may Allah be pleased with him)." (Al-Majmoo‘ 1/512).

This view was also favoured by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him), who said: That is because the hadiths speak of the non-traveller and the traveller wiping over their khuffs, and it cannot be said that someone wipes over them unless he actually does that, and this is the correct view. " (Ash-Sharh al-Mumti‘  1/186).

And Allah knows best.