Unfortunately, no. The best you can hope for is exporting your Pro piece as a DV-AVI and then importing that DV-AVI into Premiere Elements.
Welcome to the forum.
As Steve says, PrPro .PRPROJ files will not open in PrE. It will work the other direction, with some caveats: Instant Movie/Themes will not work. Some Transitions and Effects will not translate.
When one tries to Open the PrPro Project in PrE, an error message to the effect of "This Project was created in PrPro. You must Open it in PrPro."
The best that you can do is Export your Project as DV-AVI Type II w/ 48KHz 16-bit PCM/WAV Audio, or similar. The exact format will depend on whether you are in an SD, or HD Project. Then, one would Import that file into PrE and continue editing.
Note: if you go the Export/Import route, do not edit the Clips too tightly, or add Transitions, unless you are certain that you will not be editing those, when in PrE. Otherwise, you will loose the Handles on the Clips.