Stereographic to equirectangulaire projection

I have this wonderful map in stereographic projection.
However, I'm no able to put that as a texture on a sphere.
A way might be to convert it to an equirectangulaire projection.
That projection is easy on a sphere.

The question is how to convert stereographic to equirectangulaire projection?
Directions how to do this in cinema 4d or Python formulas are very welcome.

Note: you can recognize the sterographic projection by looking at the poles.
The poles are not one point, but stretched over the whole width.

First picture is an example of an input stereographic map.
Second picture is an output example of a equirectangulaire map.

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