Step 1. Defining unknown CRS
I would suggest double-checking if suddenly there is a
prj-file, placed in the shapefile location.
If not, you can try using projfinder. For instance, when one tried it with provided coordinates
There are two options:
I would proceed with EPSG:31467 because EPSG:31463 is not maintained anymore.
DHDN / 3-degree Gauss-Kruger Zone 3
WGS84 Bounds: 7.5000, 47.2700, 10.5000, 55.0600
Projected Bounds: 3386564.9400, 5237917.9109, 3613579.2251, 6104500.7393
Scope: Large and medium scale topographic mapping and engineering survey, cadastral survey
Last Revised: Sept. 24, 2008
Area: Germany - 7.5°E to 10.5°E
Step 2. Changing unknown CRS into WGS84
It is already a well-known topic in the GIS domain. So, I would highly suggest to simply searching it online.
There are several references that I may point out:
Step 3. Overlaying with another shapefile
The vital trick is that all of your shapefiles that have to be overlapped must match the same CRS.