Brainshark's conversion process transforms PowerPoint slides to images. You are not able to extract the source file from a Brainshark presentation.
However, in our March 19, 2016 Product Release, we added a feature that now Auto-Saves your PPT file as an attachment to your content upon upload.
When you upload content to Brainshark, Brainshark creates a copy of this content in the Attachments tab. By default this attachment will not be available to viewers of the presentation, but you can click edit for the attachment and turn on “Show link on attachments tab”.
Note: If your decks are not saving as attachments to your Brainsharks, your Company Administrator may have disabled this feature in your site. If you do not know who your Company Administrator is and you would like to request this feature in your site, you can reach out to Brainshark Support (firstname.lastname@example.org) and request that they put you in touch with your Administrator.