Peter's "prophecy" about Remus finding his mate was supposed to be a joke.

So why is it coming true?

Time period: Marauders Era. July 1978. The Marauders have just graduated.

"When the full moon blooms twice

In the heat of July,

The wolf will find his mate

As they soar through the sky."

When Remus realized that 1978 would, indeed, see two full moons that July, right after he and his mates graduated from Hogwarts, he started to wonder if Peter had perhaps been onto something after all. Peter assured him that his third eye was as firmly closed as a hinkypunk's kneecap (whatever that meant) and that it was a bizarre coincidence that he shouldn't read into.

But if Remus was good at one thing, it was overthinking. That "prophecy" haunted him for the better part of his final term at Hogwarts. When the Marauders gathered at Potter Manor for the second full moon of July, Remus couldn't help but feel a sense of eager anticipation. He watched James transform into his stag animagus form, Sirius become a big black dog, and Peter turn into a rat.

Historical note: There were, in fact, two full moons (often referred to as a blue moon) in July 1977, but I moved it to the next year to be after graduation.