I need to transform an old logo into a vector and raster image

I need support to transform an old image we have into a more usable vector and raster image.
The usage is not sophisticated: we just need that for our microsoft templates (powerpoint, word, etc.)

It is requested to start from an image (and a photo) and reconstruct the logo into the suitables files format. The logo is in black and white.

Thanks in advance for your reply.

Please let me know if you can do a flat offer