Take the gift and "give" it to the rightful owner. Then sit down with your daughter and write a letter to Santa and mail it off.
When its Christmas and the local mall has a Santa, have her ask Santa for the gift. Tell Santa what the circumstances are so he can help her realise if she is a good girl that he will bring it to her.
Look at my profile photo. I've played Santa for about 15 to 16 years. The last three years were with my own beard. I get requests like this occasionally and always play it up big for the child and the parent. HINT: Bring your girl early to see Santa. The closer it gets to Christmas the less time he will have to work with you and your daughter. If you were coming to see me, I would say to come by 30 minutes or so before you arrive with her and tell me so when I see you bringing your daughter, I can call her by name and mention that I loved her letter and other things. I ofter have time to remind the kids that they should be helping their mom by setting the table and carrying out the trash and putting their dirty clothes in the dirty clothes, etc. When we have time the kids and I talk about getting homework done and other such things. I've even had very prepared parents bring me the letter the child wrote to Santa and Mailed off ;~)) so when I speak with her I can bring out the letter an tell the child, "See, I have your letter right here."
Good luck to you and yours.
P.S. I love playing Santa and seeing the sparkle and wonder in kids eyes.