When the user clicks the button at the end of the eventhandler you can use
Response.Redirect(urlToPDF);
For this to work you will need the PDF to be in a folder where the user can browse to.
If you leave the content-type default the browser will probably open the document like normal, but it might download it if the user has his settings on that.
If you want to force a download, and leave the user on your page, you will have to change the http content-type header to application/octet-stream.
To change the http header you can use the following code.
Response.ContentType = "application/octet-stream";