Try packaging (File > Package). If the printer won't accept PDF files, that's the best way to send the assets along with the InDesign file. If you have InDesign CC 2014 or 2015, it also includes the IDML file along with the assets in the same folder.
Hi Steve did you get my reply? I did as you said and I'm sending you screen shots to see what I discovered. Isn't the file embedded per screen shot? This may sound like dumb question but if the image is a psd it should be okay right? Also here are the files I emailed the client and client forwarded to printer. Do you know why a printer would ask for a idml file? I'm not in communication with printer my client is. I'm assuming because the printer must use the idml indesign file so he can change the names/titles on the business cards.
before packaging the document, un-embed the placed PSD image.
Then do the packaging with options [x] Include IDML and best [x] Include PDF so that the printers have a chance to check by opening the PDF if everything is alright and the layout is preserved after opening the IDML.
Send the package as a zip archive format to the printers.
I sent my client & printer idml files. Printer says the images aren't linked.
If the images are embedded then the printer doesn't need the image files—they're embedded. If for some reason they want to edit your images they can unembed without the originals via Unembed from the Links panel. Linking vs. embedding has no affect on output quality.
Your screen capture shows the image type as RGB, so they may feel the need to convert the images to CMYK, but again they don't need a linked file to do that. The conversion to the correct CMYK space can happen on Export or Print.