Couple things...

1. Turns out he got canned in the summer of 2019 (6 months in to the job!) and moved from CA back to Illinois: IRC §217 generally requires taxpayers claiming the deduction to satisfy both the time and distance tests.  The regulations do provide for limited exceptions and my presumption here is that your client had reasonable expected these test to have been met if not for an involuntary separation that must be be the result of willful misconduct.
2. I have a client who has approx $20,000 in taxable moving expenses paid for by his employer: My big question is what was paid exactly.  Doesn't matter at all for federal but it sure does for CA purposes because qualified moving expenses need to be distinguished from all else, which would remain fully taxable.
3. California is one of a few states that still allow the moving expense deduction: That doesn't tell the whole story, CA also conforms to IRC §312(g) effective as of Jan 2015.  This means your client has nothing to deduct so long as the employer administered an accountable reimbursement plan (if not direct payment) for qualified moving expenses and excluded those fringe benefits from taxable CA wages.
4. Looks like you also get a partial deduction (based on the ratio of CA wages to all wages) even if you move out: No, you generally don't.  By case law, moving expenses have their nexus with the new job and, therefore, a forward attribution.  To the extent the new job's compensation is not taxable to CA, no deduction should be allowed.  This could be different if reimbursement for relocation expenses from CA to IL were covered by the employment terms with the CA employer.
5. If you moved out of California in connection with your new job and received compensation from that job attributable to a California source, your moving expense adjustment will be limited by the ratio of California source compensation from the new job to total compensation from the new job: The key phrases in this are "attributable to a California source" and "California source compensation", which jive with what I explained in #4.  If your client's IL employer paid for the move, employment with that employer commenced only after the termination of CA residency, that employer made no payment to your client during his CA residency, and your client did not perform any services in CA for or on behalf of that employer at any time, there is generally no CA source income as defined in the CA R&TC and its regulations.  Hence, the numerator of that ratio will be $0 and that will result in $0 deduction.