It has been narrated in “Mukhtasar tareh madinatul dimashk” (1/2515):

عن أبي عمرو بن ذكوان قال قلت لعائشة ة رضي الله عنها من سمى عمر الفاروق قالت النبي عليه السلام

From Abu Amr ibn Zakun: “I said to Aisha, may Allah be pleased with her, who called Umar – al-Faruq? She said: “Messenger (alaihi salam).

And it has been narrated in “Mukhtasar tareh madinatul dimashk” (1/2515):

عن ايوب بن موسى قال قال رسول الله صلى الله عليه وسلم ان الله جعل الحق على لسان عمر وقلبه وهو الفاروق فرق الله به بين الحق والباطل .

From Ayub ibn Mosa in mursal form: “Prophet of Allah, sallalahu alaihi wa ala alihi wa sallam, said: “Allah placed truth upon tongue and soul of Umar, and he’s faruq, Allah differed by him between truth and falsehood”.

Words that shias use to quote from ibn Shihab, that first one to call Umar – al-Faruq were ahlalkitab, were narrated in balaghat form. Meaning without chain. I don’t claim that above two mentioned stories are authentic, but one of them is at least has chain till prophet (sallalahu alaihi wa ala alihi wa sallam).