magpiejoe08
Contribution Based ESA is not affected by the claimants assets and savings so there would be no problem with you giving money to your family.
However, if you are in the WRAG and receiving ESA(CB) then your payments will be limited to 365 days, if you are also eligible for Income Related ESA at the end of the 365 days then you can be switched to ESA(IR) and payments will continue. Disposing of your savings before this switch may be viewed as having been done in order to obtain eligibility for ESA(IR) and count against you.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems