I am not sure why you think the law would, or should, hold Google liable for the reprehensible conduct of someone who misappropriated your husband's identity and utilized it to harass you.
In order to sustain a claim your husband must show that; (1) Google owed him a duty of care; (2) that Google's action or inaction constituted a breach of that duty of care; and (3) as a direct and proximate result of that breach, he suffered compensable damages.
I can't imagine how you would show that Google (a search engine) owed a duty of care to your husband to actively prevent identity theft or harassment. Your husband would be better off consulting with a lawyer about suing the perpetrator.
I don't think Google is the right party to sue. If you know who did it, and can show actual damages, then you may have a claim worth pursuing.
This is not legal advice nor does it create an attorney-client relationship. This is for education and informational purposes only. It is always recommended that you contact an attorney with any concerns as each individual case is unique.
It is unlikely that any experienced litigation attorney would agree to accept this matter on contingency. The prospects for a successful result -- which is THE critical issue for a contingent fee agreement -- are immeasurably low, for many more reasons than space here will allow. But here are just two: you don't know the perpetrator's identity? Then you can't produce him/her as a witness, an essential piece of the claim you theorize here.
Second insurmountable problem that will stop any lawyer from gambling here with his/her time and effort: : the law insulates the publisher (Google) from liability on these kinds of facts. Google is (1) not expected or required to read or verify everything that it hosts, so says the law; and (2) not required to take your word for it when you notify them about your contention of fraud.
If you were writing the laws, you might not have given internet publishers a pass on being held legally accountable for the content of the matter they host. That's a legitimate policy position. But Congress did give them that legal pass, and that is the state of the law. That law will cause any complain you can succeed in serving to be swatted away as a nuisance by the skilled army of Google attorneys. That's not a formula for obtaining legal representation on contingency.
If you are determined to pursue this claim, you will need to do it as a pro per or to fund it from your own financial resources.
No doubt there are many horrific and unforeseen crimes and frauds enabled by the internet and the strange tapestry of laws that half-heartedly govern it. But the law is still evolving in this vast subject matter and is not anywhere near "equilibrium" or resting point.
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