If the person started wiping over his socks or khufoof when he was at home, and some of that period (which is 24 hours) still remained, then he travelled, he may complete the period for the traveller to wipe over his socks, so he may complete three days and nights starting from the time when he first wiped over them when he was at home.
This is the view of Imam Abu Haneefah and it is one of the two views narrated from Imam Ahmad (may Allaah have mercy on him). Imam al-Shaafa’i was of the view, which was also the other opinion narrated from Imam Ahmad (may Allaah have mercy on him), that he should complete the period of the non-traveller.
The correct view is the former, because the Prophet (peace and blessings of Allaah be upon him) granted a concession to the traveller allowing him to wipe over the khufoof for three days and nights when travelling.
See: al-Mughni (1/371); al-Insaaf (1/402) and al-Sharh al-Mumti’ (1/251).
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said:
If he wipes over his socks when he is at home, then he travels, he may complete the period during which the traveller may wipe over his socks, according to the correct view. Some scholars stated that if he wipes over his socks whilst he is at home and then travels, he should complete the period during which the non-traveller may wipe over his socks, but the correct view is that which we have stated, because this man still had some of the period for wiping over his socks left before he travelled, then he travelled, so he comes under the ruling of a traveller who may wipe over his socks for three days. It was narrated that Imam Ahmad came back to this view after he used to say that he should complete the period of the non-traveller. End quote.
Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen (11/175).