How to synchronize a Windows database for Linux?
A single time syncron can be done by simply dumping the database on the Windows, and piping into a command line postgresql client to your Linux machine:

pg_dump --host=your.windows.host --port=5432 --user=you|\
psql --host=your.linux.host --port=5432 --user=you


If you are thinking on some type of replication cluster, then it is hard to answer here, but you could read the docs.

There is no major OS-dependence in the storage areas and protocols in PostgreSQL, but these are enough to make the cross-os physical replication impossible (ref). From PostgreSQL 10, you could use logical replication, or use some third party solution.