It is better to give a gift. You can give a customized name necklace. Just think of it as a gift given by you and your girlfriend. This gift is very creative and special. It seems that there is only this one in the world. Isn't it very special? Every woman likes to have a unique gift in the world. This just satisfies her sister's strong curiosity.
It is also good for you to send a customized cake for her sister's birthday. It is best to give her sister the flavor she likes. It doesn't matter if it is expensive. Her sister is happy. Many stores also allow DIY. In order to let her sister see your intentions, I suggest that you and your girlfriend make a cake together. It is more thoughtful. Her sister will be moved by you and leave a good impression on her, which will be convenient for the future.
More practical gifts like perfume, clothes, and various more luxurious gifts should also be liked by her sister. It is better to call your girlfriend to ask her opinion and buy gifts for her sister together. After all, she still understands her sister's hobbies and so on, and it is more convenient to buy gifts.