While you cannot add a slideshow without uploading the image files again to the new page, you can include a gallery from the post.
http://en.support.wordpress.com/images/gallery/

type this in the visual editor:
[gallery id="NUMBER_ID_OF_THE_POST"]
Where I typed NUMBER_ID_OF_THE_POST type in 1420

so the photos stay in focus

If your reason is to highlight that post and keep it prominent, you could add a single image from your media library to the page. Link the picture to the post rather than to the image file itself.

Another way to make that post important would be to use a text widget in your sidebar with an image from the post linked to the post itself.

WordPress.com's slideshow feature shows all photographs that are attached to a post. The only way to duplicate a slideshow and place it onto another post or page is to re-upload all of the images to that post or page, then embed a slideshow there.

Best,
P.

I run a website for our building, and we have a blog post with lots of lovely photos from the backyard. I want to copy the slideshow into one of the (already existing) static pages the site consists of too, so the photos stay in focus. I can't seem to find a way to do that. I can't find any identifying features of that particular slideshow to help the page recognise it.

Is there really no way to do this, do I have to delete the page and re-write it - inserting all the photos again?

This is the post with the gallery/ slideshow: http://soylegarden.wordpress.com/2012/08/12/det-bugner-i-bakgarden/

This is the page I wish to include the slideshow: http://soylegarden.wordpress.com/a-bo-her/hagegruppa/

Thanks for your help:)