Raven could be integrated by having a common enemy. Let's say there's a powerful being that wants to conquer both the magical world of Harry Potter and the superhero - filled world of the Avengers. Raven, with her own set of powers that combine elements from both worlds, is the key to stopping this enemy. In the Harry Potter side, she could teach the students some new ways of combat magic that she learned from her experiences in the Avengers' world. And in the Avengers world, she could use her knowledge of Hogwarts' magic to create new defenses against threats that are related to magic.
In fanfiction, Raven could be an interesting addition to the Harry Potter and Avengers universes. Maybe she has some sort of magic ability that links her to the wizarding world of Harry Potter and at the same time, she might possess powers that could make her fit into the Avengers' world. For example, she could be a powerful witch who also has enhanced physical abilities like the superheroes in the Avengers. She might interact with Harry Potter characters by using her unique powers to solve some magical problems at Hogwarts. And in the Avengers' side, she could be a new recruit with her own set of skills and backstory.
Raven could be an ancient and powerful witch who has been living in seclusion for centuries. She might have noticed Harry's special aura or his connection to powerful magic and decided to adopt him to pass on her knowledge.
Harry Potter might save the Avengers by using his magic to teleport them away from danger. He could use Apparition or the Floo Network if he could somehow make it work in the Avengers' world.
Harry Potter could lead the Avengers through his strategic thinking. He's had to plan against Voldemort and his Death Eaters. So he could come up with battle plans for the Avengers. He might use magic to communicate with the team over long distances, like a modified version of the Floo Network. Also, he would encourage the Avengers to embrace their individual strengths, just as he did with his classmates at Hogwarts.
He could use his invisibility cloak for stealth missions with the Avengers.
Well, Harry Potter might assist the Avengers in fanfiction by providing unique forms of transportation. His ability to apparate or use the Floo Network could be a great advantage for the Avengers. Also, his experience in fighting dark magic could give the Avengers new strategies against their powerful foes.
His magic could be integrated by using spells for combat. For example, 'Stupefy' could be used to incapacitate enemies quietly. And for reconnaissance, he could use 'Alohomora' to unlock doors and access areas without being detected.
His magic could be used for stealth. For instance, the invisibility cloak could be a great asset for MI6 agents on secret missions. They could move around unseen by the enemy.
One way could be to have it play during a Quidditch match that has a special international or Muggle - related event. Another way is to have a wizard or witch who is a big fan of Muggle culture and they sing it during a celebration at Hogwarts.
They could be integrated as a new form of magic that the characters discover. For example, Hermione might find a book in the library about the cards and their connection to ancient magic. Then the characters could start to search for the cards and figure out how to use them to their advantage in their battles against the dark forces.