Aben Reshef, the scribe said:

Here is the text of letter that was found in the end of this Torah addressed to rav Tovyahu ha-Baki, the son of the honourable rabbi Moshe ha-Avel, may is his soul in the Garden of Eden; this letter was sent to him from the holy city of Jerusalem in year 1321 of the Seleucid era or year 4789 from the creation of the World (here is most probably a print error because Seleucid year match with year 1010 according to Christian date but Hebrew year match with year 1029 - note of translator), and was found in the book storage room of our holy community of Bene Miqrah in Gezlev (Gözleve, Kezlev, Yevpatoriya; Crimea), may bless this community its Fortress and its Redeemer.

In the Name of God of the World, the Holy of Israel.

Shalom Dear rav of our brothers in the Covenant, rabbi Tovyahu ha-Baki, the sage and the judge, who loves the Torah of God and who keeps her commandments, the son of rav Moshe ha-Avel, which soul is in the Garden of Eden, who is the rav of community Bene Miqrah in Constantinople, may protects them their God in these days as same as in the days when the messiah will come on Zion.
Amen.

You asked me in your second letter how we determine months and when we begin to count Omer; from your questions I conclude that you did not receive from us all books (written) by our ancient (authors).
Know, that we from the time of our master Anan ha-Nasi, the Head of Exile, may he is blessed by his brothers, determine a new month on the base of visibility of New Moon during the evening time, after the rise of this New Moon; and we determine the beginning of the month Nisan on the base of discovery of (barley) ears, that announce (by stage of ripeness) the beginning of month and Omer of Pesah, then we have the common year with twelve months.

On 23 of Shevat we use to survey the barley crops in the fields of Aram Naharaim and Damascus.
And if we see that the ears were formed on the straws, we start to count from 23 of Shevat 50 days till Pesah.
In this case we have an incomplete Adar and we know that on 14 of Nisan will be ears ripened and ready for harvest.
But if we do not find the ears on the 23 of Shevat, we know from experience that the ears will not be ripened in Nisan, and in that year we use to add Shevat to Shevat, to have Purim in Adar and Pesah in Nisan, not in Iyar.

Also outside of the Land of Israel our brothers in the Covenant use Maḥzor composed beside the good fig trees, during the Babylonian Galut in the time of our master the king Yekhanyah, peace with him, and (in the time of) prophets, peace with them.

Calculation of Maḥzor is derived in accordance with the appearance of barley ears in the land of Israel, to be possible to fulfil the commandment to observe the month of barley ears.

The beginning of months they also determine on the base of visibility of New Moon, not on the base of astronomical new moon as do it our brothers Bene Miqrah.
The counting of Omer, both (we and as same as they) start in accordance with the clear sense of written (Law), from the first mimaḥarat (Shabbat) till the seventh mimaḥarat Shabbat; in the same way as our ancestors in the time of the first Temple, Babylonian exile and also in the time of the second Temple.

But three hundred years after the construction of the second Temple this topic caused separation (of Israelites), because the soferim (scribes) and perushim (Pharisees) fabricated own new law and they became to start the counting of Omer (on the base of system) mimaḥarat yom tov, from evening of 16 of Nisan, it means they changed the sense of written (in Torah).

Only Tseddukim, who did not believe in the life of the soul after death, in the reward and in the resurrection of deceased, and Boethusians, they counted Omer (on the base of system) mimaḥarat Shabbat, it means from Shabbat bereshiit.

And all was as was written: and huge enmity is between them.

And when our master Shehanya Ḥizkiyya ha-Nasi, the son of Ovadya ha-Nasi, saw that dissension between Perushim and Tseddukim intensified and caused the destruction of the Holy City, he took his son Shemaya ha-Nasi and whole his family, and the book of Torah that he inherited from his royal ancestors and that was transcribed from the copy of (original) Torah of Moshe in the time of kingdom.

And with him went many of Israelites who feared the words of God, they returned back to Babylon, and they settled in the towns near Bagdad; they were saved from the fire of discords, that flared them (Tseddukim) and Perushim.

Regarding counting of Omer, at least Pineḥas the Pious, honour to his memory, the son of Yair, may he finds blessings among his brothers, interpreted mimaḥarat Shabbat in accordance of (sense of ) Torah, it means as Shabbat bereshiit, as well as other before him, but they did not agree with him.

(Written in) year 4789 - (it means year 1029 of civil era)

Aram Naharaim - the north of Mesopotamia