Hello,
just copy the whole directory of your calculation from the Linux box to your Windows system. TmoleX does not need to read in the output file, as all results are stored in the control file or files referenced by it (like the vibspectrum file).
Then, in TmoleX, use File -> Open Job/Control File to read in the control file. Switch to the Results panel. The buttons on the right side (vibrations , IR spectrum, thermochemical properties, etc. should be accessible).
Regards,
Uwe