I was wondering if it is possible to share a Module loaded into the Master Site's Article with the Slave Site?

I have a Master site with a plug-in that allows you to Load a Module into an Article Content Area. I loaded a module into the article on the Master site. Then I installed the plug-in into the Slave Site through the Multisites Component. I then Linked the Master Site's Article on the Slave Site through the Multisites Article Share Component. The Slave Site now shows the Article text from the Master Site but, not the module loaded in the content area from the Master site. Is there someway to get the module to read from the Master site vs. the Slave site location?

No this is not possible.

Any plugin marker that could be present in an article will be resolved by the plugin in the specific slave site and therefore get the content from the slave site.

In your case, you must have the module duplcated in the slave site and you have to duplicate its content.
This is true for any plugin.