@Just-Lisa-Now- "I'd be tempted to put it on the return (to avoid the CP2000 in a couple years)"

I would have the client sign a waiver first:

"I understand that tax practitioners have no knowledge of the algorithms used by IRS to select returns for audit. This includes whether an additional $______ income reported as having been received, when it was not, and a subtraction of $_______ , when there is no basis for such a deduction, will ultimately lead to my return being audited when otherwise it would not be.  I agree that this is being done to avoid a half hour of work to respond to a computer notice that might be issued by IRS, which is already well aware that many 1099-G forms are issued because of fraudulent unemployment claims."

But my question here is, what makes you think the 1099-G is going to be mailed to the taxpayer whose identity was stolen, anyway?  1099-G forms can be delivered electronically, with consent:

"Electronic recipient statements. If you are required to
furnish a written statement (Copy B or an acceptable
substitute) to a recipient, then you may generally furnish
the statement electronically instead of on paper, but only if
you meet the requirements discussed later in this section."