The euphonium and French horn both have different transposition levels. The euphonium typically plays in C making it a non-transposing instrument. The French horn, however, is not a non-transposing instrument and sounds in F, which means the sound produced will be a perfect fifth lower than written. Because of this, if you were to give a French horn player euphonium music without transposing, the French horn would play the notes off by a fifth.
Learn how to transpose up a perfect fifth. The perfect fifth consists of seven half steps. With this knowledge you can determine that a perfect fifth above Eb is Bb. While A# is also seven half steps above Bb, you would use A# because A is actually a fourth away from E. Transpose every note from the euphonium part up a perfect fifth.
Determine whether the transposed part is within the range of the French horn. In most cases, this won't be a problem since the horn can play the entire range of the euphonium. However, if the part uses notes below E two octaves below middle C, you will have to transpose the music up an octave.
Tips
If the euphonium part is in treble clef, that means the euphonium is written in Bb and not C. This requires that you transpose up a major sixth instead of a perfect fifth for a total of nine half steps.
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