Yes he can give the gift without any issues, gift is exempt from tax. Also sister needs to show in ITR under exempt category, hence no tax liability. Even brother doesn't face any issues, for brother no need to show in ITR.
In addition to Jain sir reply , I would like to add that , it's better to prepare registered Gift deed , always in future also . it's exempt Income as per section 56(2) of the Income tax act .