Photoshop Elements and Premiere Elements are standalone products. Each coming with its own Elements Organizer.
When you had Photoshop Elements 9 and Premiere Elements 9 on the same computer, they shared the same Elements Organizer 9.
When you have Photoshop Elements 13 and Premiere Elements 13 on the same computer, they will share the same Elements Organizer 13.
Now here is the core of the matter:
1. What do you now have on your computer
Photoshop Elements 9 and Premiere Elements 9
Photoshop Elements 9 and Premiere Elements 9 (means Elements Organizer 9) and only Premiere Elements 13 (which means Elements Organizer 13 also)
2. The Elements Organizer 13 Slideshow feature is drastically different than the Elements Organizer 9 Slideshow feature.
Although you can convert the Elements Organizer 9 in Elements Organizer 13, Elements Organizer 13 Slideshow Builder will not accept the Elements Organizer 9 slideshow unless you agree to convert it into the new Elements Organizer slideshow format.
The Elements Organizer 13 Slideshow Builder has less opportunities than the one you are used to in 9. And, it does not integrate with Premiere Elements Editor the same. 13 will give you AVCHD.mp4 720p or 1080p slideshow file with a choice of a few Adobe pre-made themes.
I would strongly encourage you to finish and output your slideshow from Elements Organizer 9 and into Premiere Elements 9 Editor.
But, please supply more details, and we will try to find the best way through this.
Add On...What problem with 9....Editor and/or Elements Organizer?