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And on Monday, she decided to share one of the sweetest post-birth moments from that momentous day with her fans, via an Instagram video:
In the black-and-white clip, we see Duff still in the birthing pool, with partner (and the baby's father) Matthew Koma leaning in from the side. And in a magic moment, the little girl opens her arms to give mama a big old hug on the neck!
"I've been wondering for a long time if I would ever share this video as it is extremely personal," Duff, 31, wrote in the caption. "(I)t was so absolutely lovely and rewarding(and shocking) that after giving birth to my baby girl we hugged ...for the first time, In my mind I like to believe that she was saying good job mom. Go team go."
Banks now joins her big brother Luca, 7, whose father is Duff's ex Mike Comrie.
"Matt provided such a safe calm strength, my mommy and sissy were there to cheer me on, and of course my birth angels to make sure all was well and big brother (downstairs deep in Legos)," she continued in the caption. "I cannot believe this day was only 5 months ago!! It seems like B has been here with us all along. The time is already going so fast..she tried avocado yesterday!"
Not every moment has been quite so delicious, though; Duff asked for help on Instagram in January because Banks was dealing with colic:
And in February, she revealed she'd used a sleep coach to help the little girl learn a sleep routine.
Still, though, a newborn's hug is hard to beat. As Duff continued, "(F)eeling blessed for this full hectic life and all the people in it. Happy 5 months Banks (oh and thanks for quitting colic) that was a doozy"