Exporting images from Ps to Ai

Thank you for your response Mohammad. Appreciate your help with this.

Here is my current flow:

* open jpg. doc. in Ps to crop image (Ps resolution is 72 pixels/inch), (W - 360 pixels, H- 304 pixels), (RGB color)

* “save as” edited jpg. image

* open new art board in Ai and “place” jpg. image

* embed image
(note: the image appears normal at this point, until I move it to the “swatches” panel)

* move to “swatches” panel
(note: when I place the image it is now distorted)

* save swatch library as Ai

* save to “user defined” swatches library

My intention is to "place" the pattern swatches into various size rectangles, squares etc. (quilt designs), the distortion is really noticeable on some rectangles that are for ex. 5" x 20" etc. , as you can see on the attached images.

Thank you so much for any suggestions you might have.

Thank you Kurt, so much for your response.  Attached are the files you requested.

I have been embedding the files in Ai to build a swatch library with fabric swatch collections. In Ps they appear as one layer files so the flatten option is not enabled. I simply "export as jpg" to Ai.