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"linking" to files from another repo

I'm working on a large closed-source project.  For one of clients, I
had to create a library that consists of some directories from
original project, and even within these directories, not all files are
used for the library.  On top of that, I've added some files specific
for this library, in separate directories and in the library repo
top-level directory.  Most of files from original project are
unchanged, and for some, I had to make some small changes (mostly to
exclude dependencies on other stuff from the original project).  We're
now switching to Git from another VCS, and I'm wondering is there any
way to automatically "link" those pieces from the main project repo
into my library repo?  So far, I would run update in the main project
repo, check is any of files that I'm using in library changed, and if
so, then I would either copy the new version of given file into the
library (if given file unchanged for the library), or merge updates
manually (if given file is one of these files that are slightly
changed for the library), and then commit all these changes in the
library repo.  None of changes in the library will ever go back into
the main project, i.e. the flow of updates is uni-directional here.
So, any support in Git to automate the procedure of updating the
library with the changes made for corresponding files in the main