Your management guy has got a bad case of pointy hair syndrome. Li ion batteries, as currently produced by quality manufactures (many fewer than you might imagine) are often specifically not warranted by the original manufacture for longer than 6 months after shipment. These cells use changing varieties of "electrolyte" (a sort of witch's brew of largely organic solvents + helpful contaminants), and without specific knowledge of the detailed nature (and generally microsturcture) of the electrodes AND the precise nature of the electrolyte brew, it is not possible to say anything whatsoever about risks of long term storage or reuse. In the case of Li ion battery cells storage below certain voltages (dependent on the contents of the cell) or above certain voltages will permanently damage electrode microstructures, and this damage will permanently reduce performance and safety margin. A reasonable test (but not guaranteed useful in all cases) might be to determine the internal resistance when discharged and when charged. This may be a useful hint. Or not. The point of the manufacture's data sheet with regard to charging and use, is to avoid these damaging conditions and to extend working life. Not all battery management circuits do this (as specified in the data sheet for the cell) and some are simply fraudulent. Even a proper battery management circuit will not be acceptable for use with this kind of Li ion cell, but not with this other. If this is not properly done, even a brand new cell might be dangerous or suffer performance deterioration.
These are much more capable (size, energy density, ...) than any other sort of commonly available battery, that they are very tempting. They are not as simple as flooded lead acid batteries, like the ones in vehicles for the last 100 years.