Female 4 pin fan header
Here's a general method for finding mating parts for Molex connectors.


Go to the Molex site and search for the Molex part number,
which is the manufacturer part number (mfr. part # for short)
In your case it's 47053-1000.
You'll get the product page.
This page in your case.
Find the section called "mates with".



  I see lots of them on fan extension cables, but none that can be soldered to a PCB. Does anyone know a type number or some information to continue my search?


In our case, there are only wire-mounted housings that mate with that type of header.