About a year ago a client came to us with an idea for an app. The project dragged on over the course of about one year because there were months when the client would seem to put the project on the back burner because they were so busy with other things. We started to think the project was dead which seemed a shame because the idea is a good one so we decided to completely re-build the app from scratch for ourselves using none of the original code at all.
The client now wants to go ahead and launch the original app that we built which is fine, we don't mind handing over all the code etc of the version one of the app. They don't know we have re-made the app completely. I think they think they own the idea of the app even though there are other companies offering the same kind of service already so they haven't exactly invented the wheel or anything.
My question is where do we stand when it comes to setting up a company and launching our re-made version two of the app on our own? We have no quibbles about handing over their app, we'd just like some advice on whether we're doing something a bit naughty and whether we're okay to continue?