I have not looked it up on GAAP lately since I have largely stopped doing work for non-profits (I only do one private foundation at this point and it is all tax basis), but I know the requirement used to be based on having a reasonable expectation of receiving the grant without restrictions = accrue grant income and a receivable in year the recipient is notified of the award.
If there are not any restrictions imposed that could hinder receiving the funds, then it is fully accrued in year you become aware of it. If there are limitations or specific requirements that must be met each period (conditional), you do not have reasonable expectation for receiving the full amount and instead record it as income when received.
Check the specific language of the award letter/letter of intent/whatever you want to call it since that is really all you can fall back on for determining if it is conditional or not (never rely on what an individual says--it needs to be based on the award letter!). It sounds like you have reason to believe the non-profit may not be eligible for the second payment, and if that is true based on it being a conditional award, then the CPA either does not have knowledge of the terms of the award or is incorrect on how to handle it.
If anything is accrued, also make sure you record it as unrestricted, temporarily restricted, or permanently restricted.