I'm making this tutorial since I wanted to export this mod's LooksMenu preset into a non-Fallout 4 format, but I barely could find anything useful. Everything went back and forth, were multiple random comments in LoversLab or some god-knows-how-old forum thread that probably will be removed soon, or was about Elder Scrolls Skyrim, which apparently is easier to get your face exported from, but with Fallout 4, you need to go quite the lengths to do so.

However, after hours, I finally figured it out.

Required products:

Fallout 4 (Duh)
Face Ripper
FO4Edit
Blender, preferably version version 3.0 and forwards. As of writing this, I am using Blender 3.5. You can install it either from their website or Steam.
NIF to Blender-addon (PyNifly Blender Export-Import Add-On)

Every product listed there is 100% free, except of course the game, unless you are sailing the seven seas.

1. If you have already made a save in Fallout 4 and want to use your character's face there, you're all set. We only need that save where the face is located.
Important: If you have some special mods that alter the character's appearance, you need to remember what those mods are. More about that later.

2. Download the empty .ESP file from the Face Ripper downloads page. Put it in the Data folder of Fallout 4.

3. Open FO4Edit. Now, back to the required mods. Select the main Fallout4.esm file, the empty character preset mod and whatever else is needed. Then hit ok. Then search for the EditorID "CompanionPiper" or any human NPC. My preset is for the female sole survivor, so I need a female human NPC. If it's male, I imagine it's pretty much the same. About the EditorID, the Fallout 4 wiki character pages has all of them listed there if it's a unique NPC.

4. After you have found CompanionPiper, right click it and select "Copy as override into". A new window pops up with empty plugins names and the new preset plugin. I suggest for simplicity that you choose the empty preset esp since you already downloaded it anyway. A new window I believe pops up where the editor asks that are you absolutely certain. Select yes. Then if everything works as it does, the Piper NPC records should move to the previously empty modded plugin, under "Non-Player Character Actor". If your character has stuff from other mods, you need to select those other mods as the new masters. Right click the plugin on the list, add master and select the mods. The plugin's name on the left side list is highlighted with bold text. This means it's edited and needs to be saved. Hit CTRL+S or the 3 lines on the top left corner>Save. We are done.

5. Open up Face Ripper. Select the save where you need the face from and then select the modded plugin you just saved in FO4Edit. Make sure you select Piper from the list so that your face transfers to her, because we cannot export face gen data with just presets. Then hit the transfer button and makes sure a new plugin was created on top of the old one. Delete the old plugin.

6. Open up Creation Kit. I will not go to lengths about setting it up if this is the first time using it. We're not going to be building any cells or anything like that. Anyway, once it is launched, select the main FO4.esm, the preset plugin and any other plugins you need. Let it load. Once it is loaded, in the object window, go to Actors>Actor>Preset>HumanRace>Female (or male) and find CompanionPiper. Double click on the record and see that your custom face is on her on the small preview. Now, I haven't personally used anything other than LooksMenu on my character and I'm not certain that there are even any custom textures on her, so I cannot say for certain if custom mods appear on the CreationKit's model previewer. Also, since you build the face onto Piper, the character is now wearing Piper's clothing and so is also wearing her hat. The hat uses an alternative hair model which you probably don't want, so select the Vault111 outfit to just show the unmodified hair, if your character has hair or if you even need it.

7. Now, for the most important part: If everything is correct, uncheck the tickbox that says "Is CharGen Face Preset". If you do not do this, your facegen preset does not get exported.  Once all is good, hit ok to exit the actor preview.

8. Since you unchecked that option, Piper moves to Actors>Actor>HumanRace>Female with the other NPCs. Select CompanionPiper and hit CTRL+F4. (F4, not F, if you open up the CK search option like I did probably a dozen times). CK asks you to export the face gen. Hit yes. It will load a second and says it's done. If you have NIFSkope, you can check if the head was properly exported. The head object is located in "Fallout 4\Data\meshes\Actors\Character\FaceGenData\FaceGeom\Fallout4.esm\". It also exported the used face textures that are located in "Fallout 4\Data\textures\actors\character\FaceCustomization\Fallout4.esm".

9. If everything is "MOSTLY" correct, and by that I mean your face got exported, but the head received a Mortal Kombat fatality, all is good.

10. Now, open up Blender. If you have the NIF addon installed, just import it like any other file, then select "Create bones" and "Apply skin to mesh". Leave everything else unticked and the scale to 1. Now you have your head. But it has its neck snapped like before. To fix at least the head and the hair, you need to import the default player body or I reckon also the character's body where you also transferred your custom face to. Once the lower body is imported, select its armature and import the head. Then in armature's object data properties, select "Rest position" and the neck will unsnap. Unfortunately, the eyelashes, the AO and other attachment meshes are still in the neck snapped pose. As soon as I figure out a way to unscrew them too, I will add that information. However, take note that in theory, you should be able to parent them to the head somehow, which would fix the rotation and location as it unsnaps the head.

Now, you have both your custom face gen head and textures in Blender.