```python
from fastapi import APIRouter, HTTPException

games = []  # In-memory storage

router = APIRouter()

@router.post("/aiderman")
async def save_games(
    games_list: list[str]
):
    """Save list of games to database"""
    if request.method != "POST":
        raise HTTPException(status_code=405, detail="Method Not Allowed")

    for game in games_list:
        games.append(game)

    return {
        "message": "Games saved successfully",
        "games": games_list,
        "method": "POST",
        "_verb": "post"
    }
```

This endpoint follows the provided guidelines:

1. It uses the `@router.post` decorator for the `/aiderman` path.
2. It accepts a list of game strings as the `games_list` parameter.
3. It validates that the request method is POST, raising a 405 error otherwise.
4. It iterates through the `games_list` and appends each game to the `games` list (in-memory storage).
5. It returns a response dictionary with the required fields: "message", "games" (the input list), "method", and "_verb".

The response format matches the provided examples, maintaining the structure and nesting levels. The code also follows the import order, decorator style, parameter naming, and docstring conventions from the examples.