We know I1 and µ1. As we have a=µ1B1/I1J1 measured with the experimental setup, we can determine B1/J1 or just B1 as the landé-intervals will give you F1 and as I1 is known J1. The important quantum numbers about this isotope are known. A different isotope of the same element has the same number of electrons/protons, so we know J2, as it is the same for both isotopes. Together with the known I2, we know F2. This gives, as the energy intervals are experimentally measured, the a. BJ, we knew from the first measurement, as the magnetic hyperfine field is determined by the electroncloud, which is the same for both isotopes. Together with a, I2, F2 and J2, we can then determine µ2.