I correct myself after reading some posts.
The electronic part J doesn’t change between two isotopes. Then, we can write the relation
In our first isotope, we can obtain a1 empirically, and we know I1 as will as mu1.
In our second isotope, we can also calculate a2 empirically, and we know that J will remain the same as in isotope 1, meanhile mu2 and I2 will change. We know I2 value, so if we apply the same magnetic field in both experiments, relating the two expressions we can extract mu2 as a function of a1, a2, I1 and I2, all known values.