I started working with the .NET world when it first became available and am an expert in both WPF and WinForms/C#. It should be a piece of cake to make the conversion.
Rather than try to fill out the rather difficult 'milestones' below, in general, this is how I'd proceed:
Acquire the original software and, assuming there are no special conditions or dependencies, build it locally.
Map the functionality of all screens, including the connections between UI elements and internal data structures.
Create a WPF application.
Populate the WPF application with screens that duplicate the functionality of the original WinForms forms.
Populate the new project with non-ui code from the WinForms project.
Connect the new WPF views with the non-ui code.
During this process the client is presented with periodic updates so as to be able to monitor progress and provide feedback.
Upon completion of the final UI replacement effort the client confirms that the application performs in the desired fashion.
Source code and funds are settled up and project is complete.