Mark where it seats in the pipe.Fit of your Mouthpiece stem
Most American horn mouthpieces have a Morse #0 taper to the stem. From horn to horn the "socket" will be narrower or a little wider. German stems tend to have a narrower taper than Morse #0. Let me know if yours is that type.
If your mouthpiece goes too far, or not deeply enough into your horn, the stem on your new mouthpiece can be cut to fit it properly. Or your present mouthpiece can be adjusted. You will need to measure this fit. (BTW: Dial calipers are very handy, whether you are a machinist or a horn player.)
Here's the way to do it:
Mark where it seats in the pipe.
Measure the mark with calipers.
Record the measurement