I'd suggest you use the (IMO) easiest approach:
- Download SFML's source (either zipped or by cloning the repository).
- Download and install CMake.
- Create the proper makefiles to build SFML, but also set the installation folder to your MinGW folder.
- Build and install SFML.
This way all SFML files will land in the right folders for the MinGW components to find them just like it happens on Linux.
Let's assume MinGW is installed in "C:\MinGW", so I'd run the following commands:
cmake -G "MinGW Makefiles" -DCMAKE_INSTALL_PREFIX=C:/MinGW C:/SFML/source
cmake --build . --config Debug --target install
cmake --build . --config Release --target install
Running these three lines will build and install both debug and release builds of SFML.