Questions and postings pertaining to the usage of ImageMagick regardless of the interface. This includes the command-line utilities, as well as the C and C++ APIs. Usage questions are like "How do I use ImageMagick to create drop shadows?".
PDF is different from 'normal' image files. The geometry value here shows the width and height at 72dpi (default density for PDF) - not the direct values of your original JPG image. This wouldn't be possible for all PDFs as it can contain several overlayed images, vector-graphics etc.
When handling PDFs, you have to specify a density that you want to read in (when you don't specify one, ImageMagick uses the 72dpi). Your original file had 150dpi, so read it with 150dpi:
identify -verbose -density 150 Image-002.pdf
convert -density 150 Image-002.pdf output.png
Other possiblity: You could trick ImageMagick by changing the density value before creating the PDF:
convert -units PixelsPerInch Image-002.jpg -density 72 Image-002.pdf
Then the PDF will show about 1226x905 even at 72dpi.
But the latter is not the recommended way.