Does the innocent person have a defamation case against the bank and/or the police?
The article is somewhat confusing and hard to grasp, but the pastor seemingly has a viable case at least against the bank. I am not knowledgeable of whether state police would have governmental immunity in NJ.
Under New Jersey law, "citizens have a qualified privilege to make statements to authorities for the prevention and detection of crime", Dairy Stores, Inc. v. Sentinel Pub. Co., 104 N.J. 125, 137 (1986).
According to the article you shared, the bank's employee
could not automatically link the check numbers to the pictures. But
the lawsuit said she offered to hand-write check numbers on the photos
of the man they determined had deposited the counterfeit checks —
My understanding of that excerpt is that the bank employee rushed to "fill the gaps" without conducting an investigation competently. The bank employee was aware of discrepancy of check numbers, which should have prompted the bank investigators/staff to do a better scrutiny.
Instead, notwithstanding the bank's awareness of that discrepancy, its employee(s) pointed fingers at the pastor, which sounds in reckless disregard of the falsity of the accusation(s) defaming the pastor. Proof of that might establish actual malice, thereby striking the qualified privilege the bank would otherwise have.
The pastor's claims of malicious prosecution would be viable as well if the false arrest eventually led a decision by the court. The article's mentions of "court date" and that "the criminal forgery charge against Edwards was dismissed" leave it unclear who dismissed the charge(s): the prosecutor or the judge.
Hopefully the pastor's defamation case is presided by honest judges. If the case is presided by crooks like judge Felon Kuhnke, whose lecture from the bench is that "[T]he state [...] anybody who's powerful" and that the rest of us just have to "stay out of the way", then the pastor's viable claims are doomed.
Edited to add
The suggested edits warrant addressing JAB's mistaken belief that "neither [judge Kuhnke's] personal failings nor Vigger's dislike of her is relevant to the answer".
Carol Kuhnke is a criminal known for helping other criminals. As a recurrent criminal whose reputation is beyond repair, Carol Kuhnke is adverse to the principle that those who have been unlawfully defamed shall be awarded remedies as provided by the law.
Felon Kuhnke herself has reflected how that principle is repugnant to her. Coincidentally, she has expressed her self-embarrassing manifesto in a defamation case she presided (see excerpt of transcript, above).
Accordingly, it is crucial for defamed pastor Edwards --and indeed for any defamation plaintiff-- to ensure that the judge who presides his defamation case truly recognizes the value of a person's due reputation.
The variety and seriousness of judge Kuhnke's "personal failings" --quoting JAB's mild way to put it-- are precisely what prevent a judge from issuing the right rulings. And where that judicial felon has an explicit preference for "anybody who's powerful", a transnational bank would in all likelihood lure her into perpetuating the harm the defamed pastor has endured.
Thus, the "uncomfortable" remark is not irrelevant. It points to a very realistic risk that pastor Edwards and his lawyer(s) should ascertain. And I made that remark upon addressing on the basis of NJ law the article's story.