It's easy, once it's pointed out, to see the connection between "ambrosia" and "amṛt". But here's where it gets interesting.
The word "amṛt" is actually a compound word "a-mṛt", because "mṛt" or "mṛtyu" means "death" (which corresponds to mort in Latin), and "a-mṛt" is literally the opposite of death, or im-mort-ality. No one reading the original definition of ambrosia ("a food or drink of the gods that confers immortality") would immediately make the connection from "ambrosia" to the word "immortality" and realise that they're essentially the same word. The lexeme that English pilfered from Sanskrit just cloned itself in the same sentence, and nobody saw that happening! It's sitting right there under our very noses, just like the hidden white arrow in the FedEx logo.
"You're so cool."