After having looked and searched into the whole IRAF/PyRAF directory to point out the directory that contains the template spectra for the stsdas/synphot package it was just a matter of a quick look at the front page of the package to resolve the issue!
As it is said: “Since the data files used by synphot in its calculations are rather large, they are distributed separately”
and they provide the links to the compressed files containing all the template data.
At the beginning we started looking into which path these files are stored since you can call each template by using the environmental variable crcalspec$template_spectrum. But this variable looks at the path where these templates are stored (outside IRAF), as it is defined (when installed) though the crref variable.