You need to create a template override for the article view - default.php template file.
Layout Overrides in Joomla.
How to override the output of Joomla core
Understanding Output Overrides
So there you can create a "modal button" for the register link, to open the registration view inside a modal window.
This blog post explains how to create modals ...
Just a note that behavior.modal uses Mootools and has been removed in Joomla 4, so I'd suggest using bootstrap.renderModal instead, which will ensure J4 compatibility.
<button type="button" data-toggle="modal" data-target="#contactModal">Contact Us</button>
I see that you have modelled your development upon this page:
However, that demo has a separation between the element with the click event and the element to be toggled.
Your snippet has the popup element nested inside of the clickable element (there is a parent-child relationship). ...
For this I'll combine two extensions: form builder and a tools to display a module in a modal
Start with the form builder like:
or your preferred form tools.
See list of form extension : http://extensions.joomla.org/tags/forms
With the form you can collect the user data and send the e-book
Only one condition, this tools should ...