The embouchure position varies from one instrument to another and there can be as many variations as there are players since no one as the same teeth and facial muscles. You don't need a "text book" embouchure position to perform well. As long as it's not completely off, it's better not to change anything if it feels good and sounds good.
Some embouchure position might feel right at this moment but cause you problems in the future so it may be necessary to tweak it a bit. However, it is very difficult to predict what will happen so you might want to seek advices from more than one teacher before you do anything to your chops. Be aware that it takes time and patience to adapt to a new embouchure position and the results are often mitigated.
Here are a few simple guide lines on where to place the mouthpiece for all brass instruments:
For the french horn, 2/3 of the mouthpiece should be above the line formed by your closed lips and 1/3 below as shown in the illustration on the left.
Trumpet and trombone players will place it more or less in the middle
Tuba players can play in the middle for better sound but can also play 2/3-1/3 as it makes it easier to reach some notes.
Don't worry too much if your embouchure position isn't like what you see in books or on pictures online. I have seen people playing slightly on the side and still sound great. Everyone is different and it's more about how you feel than how it looks.
Unfortunately, some teachers will have their students change their embouchure position into something that works perfectly for them but isn't necessarily what is best for the student. They end up doing more damage than good. I've seen many people with a fine tone losing their sound, strength and self confidence after studying a few months with a so-called great teacher who made them change their perfectly fine embouchure. Don't let this happen to you.
If you do choose to make a change, consult two or three teachers. Be patient as it will take time for your lips to unlearn what they are used to, adapt to the new feeling and build new muscles. Monitor your progress over weeks/ months and tweak the new position to make it your own. You will get better results this way.
I am associate principal horn of the Singapore Symphony Orchestra and the author of the progressive methods. I'm happy to share my experience as a horn player and teacher with you.