The executor has no authority to make "bequests" not listed in the will; his job is to "execute" the will, nothing more, nothing less. Any attempt to do anything else will rightly result in legal action against him by the beneficiaries or the State.
If a claimant wishes, s/he may pursue a challenge to the will through the courts and let the courts decide the issue. The executor needs legal advice.
Sorry, I forgot to say that any beneficiary who wishes can of course make a gift to this claimant after their inheritance is settled on them. This has nothing to do with the executor, the estate or the other beneficiaries.