The best trick I found for a smooth transfer was using a folded receiving blanket for my baby’s head. When it was time to breastfeed him, I’d put the rectangular blankie on my forearm and then lay his head on it.
First, it would prevent him from sweating all over me, especially in the summer. Without the blanket, I’d get an imprint of his ear on my arm and his skin would stick like velcro. Not a good thing if you’re trying to gently transfer him into the crib or next to you in bed.
Second, as I would scoop him up and place him in his bed, I could easily slip my other hand under his head to release my forearm without tugging at his hair or folding up his ear.
Third, his cheek would have the warm blankie to lay on, and he wouldn’t get jolted awake by a cool bed sheet.