Ash Shaykh Abdul Hameed Al Hajooree mentioned in his book on the rulings pertaining to Eid,
“Congratulating one another on Eid
It comes from Abu Umamah al Baahilee رضي الله عنه that on Eid he used to say to his companions
قبل الله منا و منكم
‘May Allah accept from us and you’
Zahir ibn Taahir reported it in his book Tuhfatul Eid as in Al Haawii of As Suyuti
Also he reported with a Hassan chain from Jubayr ibn Nufayr رحمه الله that he said the companions of the messenger of Allah صلى الله عليه و سلم , when they would meet on the day of Eid, they used to say to each other
تقبل الله منا و منكم
At Tabaraani reported in Ad Duaa from Shuabah ibn Al Hajaaj who said, ‘I met Yunus ibn Ubayd so I said, “تقبل الله منا و منكم”, so he said to me similar to it.
Ibn Hibban reported in Ath Thiqaat from Ali Ibn Thaabit who said, ‘I asked Maalik regarding the statement of the people on Eid, “تقبل الله منا و منكم”. He said the affair has not ceased to be as such with us. These narrations are all reported in the treatise Wusool Al Amaani Bi Usool At Tahaani of As Suyooti with the checking by our Shaykh Yahya, may Allah preserve him.
Shaykh Ul Islaam said that [regarding] the congratulating on the day of Eid, they should say to one another after the Eid prayer, “تقبل الله منا و منكم و لحاله علينا” or similar to that for this has been relayed from a group of the companions that they used to do it and the scholars such as Ahmad and others have permitted it.” End translation. [al Majmoo 34/253]
However Ahmad said, “I do not initiate anyone with it, If one initiates me, I reply to him That is because to reply to the greeting is obligatory. As for starting with the congratulating, then it is not a Sunnah which is commanded nor is it from that which is prohibited from. Thus the one that does it has an example and the one who leaves it off has an example. Allah knows best” End translation.
Majid Jawed Al-Afghanee