I have two shapefiles representing the same GPS track taken at different times. However, they have different coordinate systems so they do not match, they are separated by about 354 meters E/W. I would like to convert them to the same coordinate system so that they overlay each other. Both were exported directly from Trimble Pathfinder Office.
Shape1 has the CRS
+proj=tmerc +lat_0=0 +lon_0=15 +k=0.9999 +x_0=5500000 +y_0=0 +ellps=bessel +units=m +no_defs
Shape2 has the CRS
+proj=longlat +datum=WGS84 +no_defs
in QGIS I saved Shape2 to the CRS of Shape1, but it did not change its position. I also saved Shape1 to the CRS of Shape2, and it also did not change its position. In both cases the two shapefiles remained separate by about 354 meters.