Fine Structure Degenerate Perturbation Theory Hydrogen

Note: We are dealing with perturbation on the states $|nlm_lm_s>$ where n is the principle quantum number, l is the angular momentum quantum number, and $m_l$ and $m_s$ are the eigenvalues of $L_z$ and $S_z$ corresponding to this particular eigenstate. j is the Total angular momentum quantum number: $j = l \pm 1/2$.

In page 275 of Griffiths, he finishes the derivation of the energy perturbation due to the fine structure correction. He then says that the fine structure breaks degeneracy in l but not in j. Why is this? It seems to me that the degeneracy in j is broken, and that there is still degeneracy in l.