I also have a license for Purebasic but suggested using Wine. Why? Because to convert to Linux, the programmer would have to choose from at least two GUI toolkits, GTK or Qt. The desktop environment such as GNOME or KDE might have a say on it too. I don't know, but I don't think it's translatable easily from Win32 API to "newer" thing. It would be better to write this presented application from scratch for Linux.
If you have read the first page of this thread, there
@Dav answers another user that he used a lot of Win32 API calls in this presented program. Also you said you're not an advanced programmer...
I don't know how it is beyond Purebasic v4.6 but back then the Win32 API functions were given the same names but with underscore as the final figure of the name, like "MessageBox_" or "CreateWindowEx_" (without double-quotation marks). If there are too many of those, instead of the likes of "OpenWindowedScreen" or "WaitWindowEvent" or other procedures designed into Purebasic for portability, and few calls to the "Gadget" library in particular (ie. using "CreateWindowEx_" or alike to create an ordinary push-button instead "ButtonGadget"), then it will be more difficult to change the app to work on Linux.
EDIT #2: One example, to prompt the user about something happening, or to answer a yes/no question. There should be "MessageRequester" in the source code to create a "MessageBox". If you see only the procedure name originally given by M$ then it will have to be changed to call the Purebasic procedure named first.
Running under Wine gives a large possible audience of people who only care about running a Windows application but cannot go into Windows at the moment. Having to run a Windows program under Wine doesn't mean it's going to be inefficient or it has a good chance of crashing. In fact, "converting" to Linux might make it even less stable if the author of the Windows application had no intention of making it portable by OS.