You could try this free module:

Inventua Shadow Module for DotNetNuke
The Inventua Shadow Module for DotNetNuke presents a read-only copy of a module from another tab. This allows the user to share content and settings between tabs.

It also allows you to present a read-only copy of a module from another portal, as long as the other portal is in the same copy of DotNetNuke.

My experience is that is works for many modules, but not for every one. Also sometimes the edit functions in the module work, but most of the time they do not. So, like Inventua say, it is only for presenting a read-only copy of a module.

There is also this module:

Module Capture duplicates another module on another dotnetnuke website. It can help you to integrate content of other dotnetnuke web site that is not in the same host of your web site. Living demo: http://www.zldnn.com/modulecapture