The motherboard would have to be removed from the device so that the micro USB port can be accessed and unsoldered from the board and a replacement be resoldered in its place.
You would need smd soldering tools and expertise to perform the repair.
Here’s the ifixit Zoom H6 Handy Recorder Motherboard Replacement guide that will help you to remove the motherboard.
Here’s a zoomed in image of the connector taken from Step.11 of the guide. It is useful to see it because there are a lot a micro USB sockets available but they are not all the same. The main differences are whether they are the “through hole” or smd (surface mounted device) type and importantly where their mounting lugs are situated on the body of the connector as this can vary as to the location and even how many there are. The mounting lugs are soldered onto the board to give the socket mechanical strength and to take the strain away from the pin connections (which are standard) which carry the power and the data.
(click on image to enlarge for better viewing)
As can be seen from the image your particular connector will have 4 mounting lugs. Search on places such a Ebay (or digikey.com or mouser.com) for a micro USB female 5 pin smd (examples only to show the different mounting lug types) to hopefully find a connector where the mounting lug location matches what you have.
Here’s a video that shows how to remove/replace a smd USB connector. This is not for your board but the principle is the same.
If doing this yourself is too daunting, contact a reputable, professional mobile phone or electronics repair service and ask for a quote. If they say that they’re not familiar with your device tell them about the the ifixit repair guide. Once they can access the port the repair would be familiar to them and they have the necessary tools and skills to do it. They may even have a compatible replacement connector as well.