Assalaamu alaykum wa rahmatullaah. We read that Sayid Sabiq wrote in Fiqh As-Sunnah:
"The conflict between miles and Farsakh is made clear in Abu Sa'id Al-Khudri's statement: 'If the Prophet, sallallaahu ‘alayhi wa sallam, traveled a distance of one Farsakh, he would shorten his prayer.' This was related by Sa'id ibn Mansur in his Sunan and by Al-Hafiz Ibn Hajar in At-Talkhis, and he implicitly accepted it by not making any further comments about it. It is well-known that a Farsakh equals three miles and, therefore, Abu Sa'id's hadith removes the confusion that arises from the hadith of Anas when he says that the shortest distance due to which the Prophet shortened his prayer was three miles."
What is the authenticity of this hadith, and does it remove the ambiguity of Shu'bah in the hadith of Anas? May Allaah reward you well.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.

The hadeeth of Sa‘eed ibn Mansoor that says, "Whenever the Prophet, sallallahu ‘alayhi wa sallam, traveled a distance of one Farsakh (one Farsakh equals 3 miles), he would shorten the prayer," was judged to be weak by Shaykh Al-Albaani in his book Tamaam Al-Minnah, as he said:

"The statement (in Fiqh As-Sunnah) regarding the distance for shortening the prayers, 'The ambiguity between miles and Farsakhs is made clear by Abu Sa‘eed's statement, 'Whenever the Messenger of Allah, sallallahu ‘alayhi wa sallam, traveled a distance of one Farsakh, he would shorten the prayer.' This was related by Sa‘eed ibn Mansoor and cited by Al-Haafith (Ibn Hajar) in At-Talkhees, and he implicitly accepted it by not making comments about it.' I (Al-Albaani) say: The author was misguided by the fact that Al-Haafith did not comment on it! As-San‘aani did the same before him in his book Subal As-Salaam, and so did Ash-Shawkaani in his book As-Sayl Al-Jarraar (1/357). However, in Nayl Al-Awtaar (by Ash-Shawkaani), the authenticity of the report was questioned, as he said after citing it, 'Al-Haafith cited it in At-Talkhees and did not comment on its authenticity. If the report is authentic, then the Farsakh would be the certain word and accordingly whenever the Muslim travels for a distance less than a Farsakh, he does not shorten the prayer even if that distance is called traveling on the linguistic and religious levels.' (3/176). I (Al-Albaani) say: How could this report be authentic while one of its narrators was Abu Haaroon Al-'Abdi, about whom Al-Haafith said in At-Taqreeb, 'He is Matrook (rejected). Some scholars of Hadeeth even declared him a liar.' This proves that it is impermissible to be misguided by the fact that Al-Haafith did not comment on its authenticity and that it does not mean that he finds it authentic, even if it is in his book Fat-h Al-Baari, which has the least number of inauthentic ahaadeeth among his books. Perhaps this is why he did not cite this hadeeth in it... and Allah knows best." [Tamaam Al-Minnah fi At-Ta‘leeq ‘ala Fiqh As-Sunnah]

As for the hadeeth narrated by Shu‘bah on the authority of Anas, may Allah be pleased with him, it was cited by Imaam Muslim and others. It reads, "Yahya ibn Yazeed Al-Hunaa’i said, 'I asked Anas ibn Maalik about shortening the prayer, and he said, 'When the Messenger of Allah, sallallahu ‘alayhi wa sallam, went out for a distance of three miles or three Farsakhs (Shu’bah is the one who doubted), he prayed two Rak’ahs (units of prayer) (i.e. shortened the prayer).''"

Imaam An-Nawawi commented on this report saying:

"His statement that when the Messenger of Allah, sallallahu ‘alayhi wa sallam, went out for a distance of three miles or three Farsakhs, he prayed two Rak’ahs does not imply stipulation (i.e. making this distance a condition for shortening the prayer). Rather, it is left to be decided according to the person's need because the Prophet, sallallahu ‘alayhi wa sallam, used not, when he traveled on long journeys, to set out at the time of an obligatory prayer and then pray it in full (without shortening it) close to Madeenah. Rather, he used to set out to travel at a time that is far from the time of the four-Rak'ah prayer, and then its time would be due at a distance of three miles or more or the like of that, so he would pray it then. The relevant ahaadeeth that are of general indications and the apparent indication of the Quranic verses in this regard emphasize the permissibility of shortening the prayers from the moment that the person leaves his town, as he is then called a traveler."

As-San‘aani said in Subul As-Salaam:

"His statement 'miles or Farsakhs' reflects doubt on part of the narrator, not a choice in the text of the hadeeth. Al-Khattaabi said that Shu‘bah doubted the exact word and that it was said that the distance of a mile is to look at a person who is on level ground without being able to tell if it is a man or a woman or other than that. An-Nawawi said that the length of a mile is 6,000 cubits. He also said that the Farsakh is three miles and that it is a Persian unit that was introduced into the Arabic language."

This hadeeth is brought forth as evidence by some scholars who held that the distance for shortening the prayer is decided according to the common practice and is not fixed. Shaykh Ibn ‘Uthaymeen said:

"The distance by which the prayers are shortened: some scholars said that it is specified by a distance, and whoever intends to travel that distance, then he is considered a traveler as soon as he goes out of his town. Other scholars said that it is specified by customary practice (what is considered traveling according to custom). This second opinion is the correct one, and it is the chosen opinion of Shaykhul-Islam Ibn Taymiyyah . This is proven by the hadeeth of Anas ibn Maalik, may Allah be pleased with him, as he said, 'Whenever the Prophet, sallallahu ‘alayhi wa sallam, went out for three miles or Farsakhs (Shu’bah, one of the narrators, doubted which word Anas used), he would pray two Rak‘ahs.' This indicates that the distance for shortening the prayers is not a two-day journey, because three Farsakhs or three miles are much less than a two-day journey. So the reference in this regard is according to custom. However, if you are not aware of the custom ... then the principle is to pray in full. Whenever the person doubts whether he is eligible to shorten the prayer or not, he has to pray it in full length in order to be on the safe side and clear himself of his liability." [Liqaa' Al-Baab Al-Maftooh]

In brief, the hadeeth (of Sa‘eed ibn Mansoor) is inauthentic, as it was classified by Shaykh Al-Albaani, and it does not remove the ambiguity in the hadeeth narrated by Shu‘bah.

Allah knows best.