So by knowing the coupling constant we know the ratio between two distances of the hyperfine levels. By Lande interval rule we can figure out the values of F of the particular levels. When we have F values of the first isotope and we know the values of I1 and m1 we can figure out the values of J. When we’ll take the second isotope the values of J will be the same,because the properties of electron could will not change (In the second isotope just the neutron number is changed,thus the electron configuration remains the same. When we consider the electron configuration we only look the Coulomb interactions). So when we know the J of the second isotope and the I2 we can figure out the magnetic moment.
I misunderstood the meaning of a. Now after watching the video a can see that a is defined in the 12 page. Thus we can measure a of the first isotope and from there calculate Bj (Because we know I1 and m1). And now when we know Bj we can measure a2 and calculate m2 ( because we know I2).