Maybe Remus did something that broke a major rule or hurt someone's feelings, and that's why he got a howler. The sender might be a teacher, a friend, or even a family member.
Well, it could be that someone was really angry with him and sent it to express that rage.
His mother is a likely sender. She could be worried about Remus and send a Howler to remind him to take his Wolfsbane Potion regularly or to be more cautious around others. Mothers are often protective, and in the wizarding world, a Howler is a rather forceful way to get your point across.
In the 'Remus gets a Howler' fanfiction, the Howler could be a misdirected one. It was actually meant for someone else but got sent to Remus by mistake. This could lead to all sorts of comical situations as Remus tries to figure out what to do with it. He might initially think he's in trouble for something he didn't do and start to worry. Then, when he discovers it's a mistake, he has to find a way to return it to the right person without getting into more trouble himself.
His mother could send the howler. In the wizarding world, mothers can be quite fierce when it comes to family reputation and she might be unhappy with Sirius's actions or friends.
Perhaps another student, like Hermione, could send the Howler in a very creative twist in the fanfiction. Maybe she has found out that Draco is planning something malicious against the Gryffindors and uses the Howler as a way to threaten him into stopping.
It could be Professor Snape. He often had a contentious relationship with Harry, and if Harry did something that Snape thought was particularly wrong or against school rules in a way that affected Snape's interests, he might send a Howler.
It could be Severus Snape. He has a complex relationship with Dumbledore. Maybe Snape discovers some of Dumbledore's plans that he doesn't agree with regarding Harry Potter. He then sends a Howler in a fit of anger to express his disapproval.
Hermione could be the sender. If Snape has made some unfair judgment in class against Gryffindor students, Hermione, with her strong sense of justice, might send a howler to him to voice her protest.
The Howler might contain Harry's anger and defiance. He could be yelling about all the harm Voldemort has caused, like the deaths of his parents and many others. It could also include threats of how Harry will stop him once and for all.
It could be Dumbledore. He was always one to oppose Voldemort and a howler from him would be a very interesting plot point. He might use it to taunt Voldemort or to try and make him second - guess his actions.
Snape could also be a possibility. If Harry did something that Snape considered a serious offense in Potions class, like using an ingredient in the wrong way that could have caused an explosion, Snape might send a howler to scold him. However, it would probably also be filled with his usual sarcasm and dislike for Harry.