Export word document with high resolution PNG to PDF

I have a nice high resolution PNG. (Download from Dropbox)
When I paste this into a new Word document, it looks good. I can’t zoom in more than 500% but at that zoom level all lines are smooth, as expected.

Now I click File > Save as and select PDF from the Dropdown. From Tool > Compress Images (right next to the save button) I select “use document resolution”. Then, I hit save.

Expected: The image in the PDF (viewed in Adobe Reader) should have a similar quality as the PNG.

Reality: The Image is much worse than the PNG. Maybe downsampled to 96ppi.

Notes:

• When I am in the save dialog and I go again to Tools > Compress Images, the selected option is reverted to “E-Mail (96 dpi)”
• I tried the same thing on a diffewrent computer with Word 2013, but no luck.
• I tried a different PDF viewer – same image quality
• I tried to encode normal 96 ppi within the PNG and resize the image in word.
• The option “do not compress images in file” is enabled. This option:
  ()
• This is a reduced problem, so please don’t suggest GIMP. My real file has some text in it. Until now I am just reluctant of redoing it all in LaTeX.
• The problem gets worse, when the image is further reduced within word. This points to a resampling going on when the pdf is created.

Additional thing I have tried:

• When I use “Printing (220ppi)” instead of “document resolution” there is no discernible difference. (After all I thought that “document resolution” means that no resampling takes place and the full resolution is used.)
• Exporting to XPS format has the same characteristics.

Question: How can I preserve the image quality when exporting to PDF?