And then join DimID with the dimension ID? I already considered doing this, but it's not possible. In the real fact table there are more foreign keys, the most typical being Date. As you can see Account 2 and Account 3 values are duplicated, so when filtering by date in the cube I get wrong values.
Sorry, but I'm not following this. If each of the dimension entries has its own ID, which it should, this shouldn't be an issue. The repetition of keys occurs with SCD 2 dimensions. This doesn't look like one of those, but you should be able to keep in separate, just like names for counties and cities are kept separate.
I'm not ruling out a many-to-many issue as the previous poster has indicated, but I'm not convinced that that must be the issue. Please provide more details if you'd like more help.