People are speed-reading emails. If you got someone willing to introduce you to someone else, and she says “send me an email that I can forward”, she is very likely to do just that, hit forward.
Don’t expect much text editing, explaining, or pitching from your contact. Yes, she know your company. Yes, she knows what you want from the introduction. The person to whom it gets forwarded has little idea. Do the hard work for her.
Writing the intro line for her (“I had a coffee yesterday with my good friend, and it struck me that the customer segment targeting positioning of their value proposition exactly matches or long-term vision for the business unit”), is likely going to have the line “See below, interested?” above it.
You are pitching for the next interaction with the person you get introduced to, not the closing of the deal itself. On the one hand, this will make writing this email a lot simpler, on the other hand, it means that you have make it super personal and relevant, a standard pitch won’t do it.