The web page Quick Links launcher just calls the default web browser to open the report using windows to choose the browser.
"On my machine" if I set Edge as default browser and set the URL of the reporting services report in the Quick Links web page option - it works.
Makes me wonder if the url ok -has it any % encoding in it?
Try copying address back out of edge after manual testing and back into the quick link URL, to check it is in the format of the URL is correct.
=======> If really stuck you could create a batch file to indirectly launch the web page in whatever browser you wish.
Using a batch file to launch web page:
Create a folder called LaunchReports on machine or network share. This will hold all the possible pages you might want to launch.
Create a text file and in the text file set the content to one of the following lines
start microsoft-edge:http://reportingservices/Reports/Pages/Report.aspx?ItemPath=/GP+Transaction+Reports/GP+Despatch+Notes/SOP_ENDespNote
The above line will launch the supplied report with edge and works for me, or use the following line which will do the same using internet explorer (32 bit version take off " x86" for 64bit).
"C:\Program Files (x86)\Internet Explorer\iexplore.exe" "http://reportingservices/Reports/Pages/Report.aspx?ItemPath=/GP+Transaction+Reports/GP+Despatch+Notes/SOP_ENDespNote"
Save the file, then rename text file to report1.bat
Now in Quick Links, select external program or file, and browse to the .bat file you just created and give the link a name.
This will execute the batch file that will in turn launch the browser with the web page as the parameter.
Now create a batch file for each report you wish to launch, probably good idea to use better batch file names than report1.bat
Messy but will work as a work around.
However I do feel it should just work with edge in the first place, which is why i think you should check your URLs . What exactly happens when you try it?
Also try, go to windows start menu and type default web browser, then click reset to reset the default web browser setup.
Tim.