Thanks votrechien (like your nickname by the way! very french of you). yes, I had the same idea. Id would settle for running both but for a limited time only just to soften the transition.
So, turns out, that the lady, who in the first place was not planning on really selling the business, suddenly feels like it is worth a lot more than I am willing to pay for it.
So I passed on the opporunity, unless she does not find another buyer. We will be focusing our energy on advertising heavily to their customers as well as increasing our range of products (which we need anyway).
I got a lot of data form her, wich is good in an way, since I have insight on what we can become with more work.