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I have done similar in the past with custom button controls but this is a standard Windows common control that you can get to work with a little massaging. It uses that awful WM_NOTIFY interface and NMHDR structure but it will end up where you can respond to it. ShellExecute() will open a browser window and its reasonably straight forward to make a link on a page or dialog that will open whatever URL you want.

Nice.  :t

invoke ShellExecute,hWin,"open","www.masm32.com",0,0,SW_SHOW

There should be also an option to get the URL directly, but so far I've not been able to spot it in the debugger :(

LITEM structure (https://msdn.microsoft.com/en-us/library/windows/desktop/bb760710(v=vs.85).aspx)

QuoteszUrl

    Type: WCHAR[L_MAX_URL_LENGTH]

    WCHAR string that contains the URL represented by the link. The maximum number of characters in the array is L_MAX_URL_LENGTH.

if SysLink control is defined with HREF like this "<a href=\"http://www.masm32.com\">www.masm32.com</a>"
that link url is filled in message.

EDIT:
https://msdn.microsoft.com/en-us/library/windows/desktop/hh298379(v=vs.85).aspx (https://msdn.microsoft.com/en-us/library/windows/desktop/hh298379(v=vs.85).aspx)
https://msdn.microsoft.com/en-us/library/windows/desktop/hh270406(v=vs.85).aspx (https://msdn.microsoft.com/en-us/library/windows/desktop/hh270406(v=vs.85).aspx)

I just used a Microsoft example. Seems to work OK, any text you like in the control, a valid URL in the ShellExecute() function. Control dumps the mouse click in the NMHDR structure into the WM_NOTIFY message and the ShellExecute() function succeeds with a valid URL.