I recommended she see my good friend Jack Miller, who is a Ph.D. psychologist specializing in healing the soul of grief.

--- Does it mean that he heals souls of their griefs, or maybe "soul of grief" is a name and it's not about healing a soul of its grief?

I take it the former way.

One way I would interpret "the soul of grief" is as "the soul when it is grieving." In other words, the psycholgist's patients are in a temporary state of grief and he is a specialist in grief counseling.

Another interpretation of "the soul of grief" is that it is "a soul that is hampered by an irrational sense of grief." This interpretation implies that grief is more or less a permanent state for the patient experiencing it. Furthermore, it means that the psychologist is a specialist in treating this kind of grief.

If the "soul of grief" is a psychological term maybe you could ask a clinical psychologist who specializes in grief counseling? I don't find a reference to "soul of grief" on google.
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 Clive's reply was promoted to an answer.
Thanks for the answers guys!