I can see this happening if I ever get hired by a competitor in the near future. I can't get into the details, obviously.
I see a current problem now that we have solved when I was with the competitor, and I know for sure, technically, that the solution[s] will work for the current company.
I agreed in a contract from my previous employer that I will not divulge specific technologies, practices, and solutions to any other entity, especially a competitor.
Personally, I feel that it's morally wrong to propose the previous employer's secret, even if I won't tell the current employer that I got the answer from my previous employer. Even if it weren't for personal reasons, I would get in legal trouble if my previous employer finds out that their competitor is now implementing their (former employer) solution.
Do I just let it sit unsolved for longer than necessary? Should I work (unnecessarily) harder to find an alternate solution?