Is Shortening Prayers while Travelling Sunnah?
Question

Is it permissible for a traveller to offer the prayers in full and pray them with four `s?
Praise be to Allah.Shortening the prayers when travelling is a confirmed Sunnah that one should not forsake, according to the consensus of the imams (leading scholars), apart from what is narrated from Ash-Shafi`i (may Allah have mercy on him) in one of his two opinions, that offering the prayers in full is preferable. However the correct view in his Madhhab is that shortening the prayers is preferable. (See: Al-Majmu` by An-Nawawi, 4/218-223) 
The view that shortening the prayers is preferable is supported by the fact that the Prophet (blessings and peace of Allah be upon him) shortened the prayers in all of his journeys, and there is no authentic report to indicate that he ever offered the prayer in full when he was travelling. 
Anas ibn Malik (may Allah be pleased with him) said: “We went out with the Prophet (blessings and peace of Allah be upon him) from Madinah to Makkah, and he offered his prayers with two Rak`ahs every time until we returned to Madinah.” (Narrated by Al-Bukhari, 1081 and Muslim, 724) 
Ibn ‘Umar (may Allah be pleased with him) said: “I accompanied the Messenger of Allah (blessings and peace of Allah be upon him) and during the journey he did not pray more than two Rak`ahs (in any prayer), and Abu Bakr, ‘Umar and ‘Uthman (may Allah be pleased with them) did likewise.” (Narrated by Al-Bukhari, 1102 and Muslim, 689) 
This refers to the beginning of ‘Uthman’s caliphate; at the end of his caliphate, ‘Uthman (may Allah be pleased with him) used to offer the prayers in full (when travelling). 
When ‘Abdullah ibn Mas‘ood (may Allah be pleased with him) heard that ‘Uthman ibn ‘Affan (may Allah be pleased with him) was offering the prayers with four Rak`ahs in Mina, he said: Inna Lillahi wa inna ilayhi raji`un (Verily to Allah we belong and verily to Him is our return). I prayed two Rak`ahs with the Messenger of Allah (blessings and peace of Allah be upon him) in Mina, and I prayed two Rak`ahs with Abu Bakr Al-Siddiq in Mina, and I prayed two Rak`ahs with ‘Umar ibn Al-Khattab in Mina.” (Narrated by Al-Bukhari, 1084 and Muslim, 695) 
Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 
“It is disliked to offer the prayers in full when travelling. Ahmad said: I do not like it. It was narrated from Ahmad that he would not comment on whether offering four Rak`ahs would be valid. There is no sound report to indicate that any of the Companions (may Allah be pleased with them) used to pray with four Rak`ahs when travelling at the time of the Prophet (blessings and peace of Allah be upon him). The Hadith narrated from `Aishah that suggests something to the contrary cannot be taken as evidence.” (Al-Ikhtiyarat, p. 32) 
Ibn Al-Qayyim (may Allah be pleased with him) said in Zad Al-Ma`ad, 1/464: 
“The Prophet (blessings and peace of Allah be upon him) used to shorten the four-Rak`ah prayers , praying them with two Rak`ahs, from the time he set out travelling until he returned to Madinah. There is no sound report from him to suggest that he ever offered the four-Rak`ah prayers in full whilst travelling. 
With regard to the Hadith of `Aishah, according to which the Prophet (blessings and peace of Allah be upon him) used to shorten the prayers and offer them in full when travelling, and that he used to not fast and fast, it is not authentic. I heard Shaykh Al-Islam Ibn Taymiyah say: This is a lie against the Messenger of Allah (blessings and peace of Allah be upon him).”
It was narrated that the Prophet (blessings and peace of Allah be upon him) used to shorten the prayers but `Aishah would offer them in full, and he might not fast one day but she would fast. 
Our Shaykh Ibn Taymiyah said: 
“This is false. The Mother of the Believers would not go against the Messenger of Allah (blessings and peace of Allah be upon him) and all his companions, and pray differently from them.”
Rather some of the Imams, such as Imam Abu Hanifah and Ibn Hazm (may Allah have mercy on them) were of the view that shortening the prayers when travelling is obligatory, and it is not permissible to offer them in full. 
However, the correct opinion is that of the majority of scholars, that shortening the prayers is Sunnah and is preferable, and is not obligatory. That is supported by the fact that `Uthman and `Aishah (may Allah be pleased with them) offered prayers in full when travelling. If shortening the prayers when travelling was obligatory, they would not have offered them in full. The Companions followed `Uthman (may Allah be pleased with all of them) in offering the prayers in full in Mina; if offering the prayers in full was prohibited, they would not have followed him in that. 
Imam Ash-Shafi`i (may Allah have mercy on him) said: “If it had been obligatory for the traveller to pray with two Rak`ahs, `Uthman, `Aishah and Ibn Mas`ud would not have offered the prayers in full, and it would not have been permissible for a traveller to offer the prayers in full when praying with a resident who is not travelling.” (Al-Umm, 1/159)
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said in Ash-Sharh Al-Mumti`, 4/358-362: 
“Some of the scholars said that offering the prayers in full (when travelling) is disliked, because this is contrary to the regular, ongoing practice of the Prophet (blessings and peace of Allah be upon him), as the Messenger (blessings and peace of Allah be upon him) never offered the prayer in full when travelling, and he said: “Pray as you have seen me praying.” This is the view favoured by Shaykh Al-Islam Ibn Taymiyah (may Allah have mercy on him) and it is a strong view; in fact it may be the strongest of the opinions. 
Some of the scholars said that shortening the prayers is obligatory and that the one who offers the prayer in full is sinning. 
What seems to me to be most correct is that offering the prayers in full (when travelling) is disliked, not prohibited, and that the one who offers the prayer in full is not sinning. This is from a theoretical point of view. 
But from a practical point of view, is it befitting for a person to do something when he fears that he may be sinning thereby? 
It is not appropriate conduct; rather you should do what is Sunnah, because that is better for your spiritual wellbeing, even if it is permissible for you to do something contrary to that.”
Based on that, it is preferable for the traveller to shorten his prayers, but he does not have the right to refrain from offering the prayer in congregation for the sake of shortening the prayer; rather he must offer prayers in congregation. If the Imam is a resident (not travelling), he must offer the prayer in full with him, and if he is travelling, he must shorten the prayer with him. 
And Allah knows best.