Transpose coordinates from pdf map onto satellite raster image

I have a map in a PDF file with boundaries that I want to plot onto a satellite image.

I have made a screenshot, saved it as tiff and imported it as a R raster object. Using click I have outlined the boundaries which I can now plot onto the raster object.

head of polygon data.frame:

> head(df)
       x      y value idx
1: 408.5 1041.5   135   1
2: 361.5  988.5   255   2
3: 344.5  997.5   170   3
4: 310.5  960.5   237   4
5: 312.5  950.5   237   5
6: 257.5  816.5   254   6

My goal is to convert the data.frame with x and y coordinates to a spatial object (sf or sp) and plot it onto a satellite image.

The problem is the projection: How do I convert my relative positions to a projection that matches that of my satellite image?

The original projection is UTM Zone 37, projection Transverse Mercator, Spheroid Clarke 1880 (modified).

(no answers on the GIS stackexchange site)