This can be done easily. But this method is not suggested though because your headset is new and you may damage the headset.
It is better to buy a 3.5mm female to male extender.
But this is the method for your information.
In this image of the 3.5mm male pin, you can see 4 connection points separated by 3 nonconducting white circles. This means there are 4 wires in this headset.
Since, you said that your headset has mic, your 3.5 pin should have 4 wires.
- Left channel -Tip
- Right channel -Ring
- Ground -Ring
- Mic -Sleeve
This is also called TRRS.
You can cut the old headset from the wire below the division of the headset. We are going to use the 3.5 mm pin of the old headset. I’m hoping that that old headset wires are good.
Then cut the new headset from the 3.5mm pin area. We are not going to use this jack.
Now use a wire stripper or a lighter to strip the wire. Since you have the same brand, connect the same color wires together.
If you are using different brand wires and if the colors are not matching, just play a song, connect the old headset to the pc and do trial and error and you will get it correct in less than 17 tries.
In the image, you can see 3 wires.
This image is only for your reference. The headset had four wires but I did not need the mic. So I cut off the mic wire.
The headset wires are too thin. So be careful with soldering, if you are attempting.
But I suggest you to buy a headset extender which looks like this. But a TRRS extender. This image shown below is a TRS extender meaning there is no mic with this extender.