What to say to a new mother:

Hadith – An-Nawawi, Kitabul-Adhkar, p. 349.

Baarakallahu laka fil mauhoobi laka, wa shakartal waahiba, wa balagha ashaddahu, wa ruziqta birrahu. [“May Allah bless you with His gift to you, and may the receiver give thanks and reach the maturity of years and be granted piety.”]

The reply is: Barakallahu laka wa baraka ‘alaika, wa jaza kallahu khairan, wa raza-qakallahu mithalhu, wa ajzala thawabaka. [“May Allah bless you, and shower His blessings upon you, and may Allah reward you well and bestow upon you its like and reward you with open hands.”]