The issue here is that Spotify gift cards are unfortunately only redeemable on normal Premium accounts. To get these gift cards added to your current Premium for Family plan, you will have to go through a couple of steps, so bear with me.
1) Downgrade your account to a normal Premium subscription. This will kick all family members off of the family plan.
2) Redeem your gift cards on your normal Premium account.
3) Upgrade your account to the Premium for Family plan and re-add your family members to the plan.
This should allow you to redeem your cards and use your Premium for Family plan. Sorry for the inconvenience. Please let me know if you have any questions! Happy listening :)
JacobRock Star 15
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I wish Spotify would just offer Premimum Family Membership gift cards! I want to give family memberships to my sisters' families. The solution you offered may be a work around but it is too much of a hassle to give as a gift. :(