Is it permissible for me to contract with another health insurance company for a lower amount to benefit from the remaining financial difference, without informing the funding entity?

It is permissible to engage in commercial health insurance when compelled to do so, or when there is an extreme necessity. It is more appropriate to consider it permissible if the state is the contracting party. It is not permissible to resort to deception to benefit from the insurance amount without referring to the granting authority, because it is a grant for a specific purpose, and thus it is not permissible to utilize it for a purpose other than that for which it was intended, except with the permission of the granting authority.