Nussach of Mi Shebeirach and Greetings by the birth of girl:

A different Nussach of Mi Shebeirach is recited for the birth of a daughter versus the birth of a son. The exact change of wording can be found in the Siddur. The Chabad custom[1], as well as the custom of Belz[2], and many other Gedolei Yisrael[3], is to bless also by a daughter with the words “Legadla Letorah Ulechupa Ulimaasim Tovim.”[4] So was likewise endorsed by Rav Moshe Feinstein as a possible Nussach of choice.[5] However, others omit the term Letorah, as women are not obligated in Torah study, and rather simply say “Legadla Lechupa Ulimaasim Tovim,[6]” or “Legadla Liben Torah Ulechupa Ulimaasim Tovim.”[7]

[1] Hayom Yom 25^th Menachem Av in quote of a letter of the Rebbe Rashab in name of the Rabbeim [See Hayiom Yom Hamevuar]; Igros Kodesh Rashab 1:210; Igros Kodesh 5:149; 12:341; Toras Menachem 2:30 and p. 77; Likkutei Sichos 2:457

[2] Az Nidbaru 4 p. 45; Minhagei Belz Eretz Hakodesh p. 76

[3] See Otzer Habris 1 Chapter 6:2-6

[4] The reason: This is based on the statement in the Talmud [Brachos 17a] that even women receive the merit of Torah study by encouraging their husbands and children to study Torah. [Hayom Yom ibid] Alternatively, it is due to the fact that the concept of the daughter in service of God is Kabalas Ol, which is the catalyst for the fulfillment of all Torah and Avoda. [Toras Menachem 2:30 and p. 77; Likkutei Sichos 2:457] Alternatively, as women are commanded to study the laws of Torah that are relevant to them, and hence they say a blessing over it in the morning, and hence certainly between man and his fellow, they deserve to receive this blessing of Torah. [Pachad Yitzchak Michtav, brought in Hakol Yoducha p. 228] Alternatively, it is because the verse [Mishlei 1:8] states “Al Titosh Toras Imecha” from which we learn that women are connected with Torah. [Minhagei Belz Eretz Hakodesh p. 76 in name of Reb Aaron of Belz; Az Nidbaru ibid]

[5] See Igros Moshe O.C. 4:67 upon the birth of his granddaughter, the daughter of Rabbi Mordechai Tendler in the conclusion of his letter that “and one who wants may add Yizku Aviha Veima Legadla Letorah Uliben Torah..”

[6] Igros Moshe ibid in his initial Nussach; Pachad Yitzchak Michtav, brought in Hakol Yoducha p. 228

[7] Pachad Yitzchak Michtav, brought in Hakol Yoducha p. 228