Dostoevsky describes Alyosha's conversion at the end of book 7. It relates to one of the main themes of the book with the corn of wheat that must die in order to bring forth a beautiful fruit. Alyosha has a life-altering moment.

"He fell to the earth a weak youth and rose up a fighter, steadfast for the rest of his life...(363)" Alyosha had this beautiful image/dream of Zosima rejoicing and then fell to the ground and rose up to become a man who is strong and knows what he wants in life.

I guess if you're a strong believe in miracles and conversion the story is believable, but if you're not then it's not. It's hard to grasp the idea that one change just change in an instant; almost as if something has possessed them. It's possible the image of Zosima really made Alyosha that happy to reach his full potential considering that is what Zosima wanted. It could also be due to the fact that Alyosha helped Grushenka be a better person and realize that she can be good. It was as if he "gave her the onion".