imported image from photoshop into illustrator changes the color

Hello,

I'm importing an image with rich black (C75M67Y65K100) from Photoshop into Illustrator. when I check the image with idropper in illustrator, the black is only 90%, not 100 as it is in photoshop.

I'm concern that when printing, the image will not appear rich black.

Note, both apps have same color space.

thank you!