What exactly do you mean by "resolve the light and heavy fragment ions"?
When Skyline extracts chromatograms from spectra, Skyline sums the intensities across a m/z channel. The width of the channel that Skyline sums across depends on your resolution or mass accuracy settings at:
Settings > Transition Settings > Full Scan
The peptide YAGEVSHDDK++ has m/z 705 in your PD screenshot, and 633 in your MaxQuant screenshot. That difference is probably because there is a modification on the Y residue in the PD screenshot, and no modification on that residue in the MaxQuant screenshot.
It sounds like you might be asking why Skyline is not recognizing the modification on the Y residue in the MaxQuant spectral library.
If you would like to apply a modification to an amino acid yourself, you can right-click on the peptide in the Targets tree and choose the menu item "Modify".
How exactly is that modification defined in your MaxQuant peptide search? I believe that Skyline cannot handle N-terminal MaxQuant modifications. That's what is mentioned in this support request:
We might be able to be more helpful if you send us your MaxQuant search results (msms.txt, and maybe modifications.xml and/or mqpar.xml). You can also send us your Skyline document by using the "File > Share" menu item to create a .zip file.
If those files are less than 50MB you can attach them to this support request. Otherwise, you can upload them here: