Is it permissible to give the husband's money designated for charity to a needy sister without his knowledge?

If your husband authorizes you to spend money on charitable causes without specifying a particular recipient, it is permissible to give some of it to your needy sister. This is, in fact, preferable, as giving charity to relatives takes precedence over giving to strangers, and they are a valid recipient of charitable donations. A woman is permitted to give charity from her own money to her relatives, and from her husband's money if he gives permission.