What happens when a living spouce has a Group Life Insurance policy from his employer.?Can it be givien to family members if stated in a will testment

No. Generally, the ownership of a group life policy cannot be effectively changed, and, to the extent it can be, doing so usually requires that the current owner complete and submit the proper forms to the insurance company. The insurance company provides any such forms. A Will will not normally be able to change the ownership of the policy. An individually owned policy is different. Ownership of an individually owned policy could be transferred by the policy owner's Will. If you are actually asking about the beneficiary designation, that has to be changed by forms provided by and submitted to the insurance company. Unless the insured person's estate is the designated beneficiary, the insured's Will will not have any control over or effect on who receives the proceeds of the policy.