@staticdev 

Have you checked if there is maybe some unused internal HP-proprietary USB connector on the motherboard? In case there is, then you could try to make or buy a suitable adapter cable.

If there is none on the motherboard, then you could try to find a cable like this 

https://www.ebay.com/itm/9pin-Male-to-External-USB-A-Male-PC-Mainboard-Internal-Data-Extension-Ca-ueW4/353305756832

and route it trough a hole or slit of the tower case, so that you can connect the TX3000E's USB to one of the external USB ports.

@woozle I found some connectors unused but with different pin numbers. Here is a photo of my mobo:

@staticdev 

Here is a link to the Maintenance Manual for your computer:
http://h10032.www1.hp.com/ctg/Manual/c04832338

Page 64 and 65 show the decriptions for the onboard connectors.

For example, the larger black one marked as "COMB" is an "optional second serial port".

Of interest in your case are only the one's marked with "USB".

The available USB connectors on the motherboard are apparently already in use for the cables that provide USB ports to the front panel of the computer. (blue connector for 2x USB 3.0 and yellow for 2x USB 2.0)

If you feel like you could live without the two USB 2.0 ports on the front panel of your computer, then you could perhaps unplug that cable and reuse that yellow connector on the board for your TX3000E card.

@woozle thanks a lot for your research and suggestion. I tried connecting the board on front-usb connector. It is not exactly the shape of the board connection and I am not really sure how to connect it.

The TP-link board connector has the shape:

OOOOO

XOOOO

The mobo connector has the shape:

OXOOOO

OXOOOO

What I tried to do is to match the X so I connected:

OXOOOO

OXOOOO

-OOOOO

-XOOOO

I am not sure it worked. Also, when I boot the computer I get the error:

Would you connect the pins this way?

@staticdev 

If the pin layout of the mainboard's FRONT USB connector is different, then it's probably a HP-proprietary connector. Apparently HP added two additional pins.

Here is link to a post from a user who connected a standard USB cable to another mobo made for HP the same way as you did and it sounds like it worked for him.

https://h30434.www3.hp.com/t5/Desktops-Archive-Read-Only/USB-pinouts-for-MSI-MS-7778-Jasmine-motherboard/m-p/3357773/highlight/true#M411999

@woozle seems promissing as I did the same. Is there a way I can check if the board is working properly? Some light or fan working maybe?

@staticdev 

I think the only way to check if it's working is to boot up the computer's operating system with the TX3000E installed and the USB cable connected to the mobo.

Do you run Windows 7, 8 or 10?

@woozle Windows 10, I also have Ubuntu. The board just works even without the cable connected. What is it for?

@staticdev 

Currently most, if not all, of these Wi-Fi 6 AX PCIe cards for desktop computers merely consist of a "dumb" PCB with an onboard M.2 socket into which an Intel AX200 M.2 WiFi card has usually been fitted.

These M.2 cards were primarily designed for use in Laptop/Notebook computers and since the M.2 connector can provide several bus interfaces at the same time, Intel opted to use PCIe for the WiFi part and USB for the Bluetooth function.

Windows 10 with an active Internet connection should have automatically installed drivers for the WiFi function and the Bluetooth function (if it was detected).

If you open the Device Manager (right-click the Windows Start button, Device Manager should be the fifth item from the top) and the Bluetooth section shows an item called "Intel Wireless Bluetooth", then it means your USB connection on the mobo works. If not, then you might also check if there is an unknown device shown under "Other devices".