There are three different episodes involved in your question.

(1) In Etruscan pictorial depictions he suckles at Hera's breast upon entering Olympos. We don't have any textual sources to give further information.

(2) In Greek textual sources the suckling happens as a baby, e.g. in Diodorus 4.9.5-7 Athena tricks Hera into suckling him when he's still a baby -- Alcmene exposes him, and Athena and Hera find him while going for a walk. This is before even the episode with the serpents. Pausanias 9.25.2 makes it clearer that the setting is Thebes, and it's Zeus who tricks Hera. There are also some uninformative allusions in Lycophron's Alexandra 39 and 1326, and Hyginus' Astronomica 2.43, which just mention that Hera suckling Heracles was a thing, with no further details.

(3) Most textual accounts of the apotheosis simply have him disappear from his funeral pyre, with a bolt of lightning consuming him in Diodorus 4.38.4. In Apollodorus 2.7.7, a cloud wafts under Herakles' body on the burning pyre and carries him to heaven.