What computer operating system is involved? Have you updated 13 to 13.1 yet using an opened project's Help Menu/Updates? If not, please consider doing that.
For your immediate question.
If you create a slideshow in Elements Organizer 13/13.1, you can export that slideshow to a file saved to the computer hard drive, AVCHD.mp4 either 720p or 1080p. The other person does not need Premiere Elements to view it - just a player that supports the AVCHD.mp4 format.
If you create a slideshow solely in the Premiere Elements 13/13.1 editor, you export it in the Publish+Share/ section of the program. There are a variety of export choices for export to file saved to the computer hard drive under Publish+Share/Computer/. The Windows Media choice would be expected to give you the smaller file size.
Just in case note, the project that you open generates a project file. If you want someone to view just your slideshow creation, then you need to export the project's edited content to a file saved to the computer hard drive or do a burn to disc. For "sendings", always consider the mode of sending and file size requirements.
If you create a slideshow solely in Premiere Elements 13/13.1 and want the other person to view and edit your work, then I would suggest that you archive the project (File Menu/Project Archiver/Copy project), and then send the saved Copied folder. This needs to be discussed further if interested in this idea.
Please review, consider, and supply more information. Any questions or need clarification, please do not hesitate to ask.