Was the story of Jesus stolen from that of the deity Alcides (Hercules)?

ou have heard of Alcides of Thebes, know it or not: Alcides is another name for Hercules. The claim has been made that Alcides was a "divine redeemer born of a virgin around 1200 BCE." From a site now defunct, we get the following (which I have verified elsewhere as well):

Hercules's mother was Alcmene, the wife of King Amphitryon of Troezen. His father was the leader of the Olympians, Zeus. He disguised himself as Amphitryon and visited Alcmene on a night that lasted as long as three ordinary nights. Zeus's wife, Hera, was furious when she learned that Alcmene was pregnant with Zeus's child. She sent witches to Troezen to stop Alcmene from going into labor, but the witches failed and Alcmene gave birth to twins: Hercule's, Zeus's son, and Iphicles, Amphitryon's son.

Virgin born? I would not try that on fathers of the girls you date, gents. How about that "redeemer" part? Just like in the cartoons, Hercules fought some battles; he liberated the folks of Thebes from their oppressors, but that's about as close as we get. What redeeming feat, we wonder, do critics have in mind?
Mark Smith in Origins of Biblical Monotheism notes an older tradition of a "Herakles" -- not the same as the Greek Hercules, actually, but because of the name similarity, often confused -- who is said by Josephus, in a passage referring to Hiram of Tyre (from Solomon's time) to have had an "awakening", but scholars are divided on what this refers to, and Josephus gives no details. Thackery reads the passages as referring rather to the building of a temple to Herakles, and nothing is said of this being's death. There is a tradition from ancient Spain [!] suggesting a death of Herakles, but his "resurrection" is described in terms of apotheosis.
One of Hercules' greatest feats, we are told, "was to clean the stables of Augeas, King of Elis, in one day. Augeas had 3,000 oxen, and his stables hadn't been cleaned in 30 years." Somehow, this reminds me of having to "clean up" after many claims like these made about Hercules!