iTunes: How to transfer a music purchase between two Apple IDs?
Short answer

No, purchases can not be transferred between Apple IDs.



Alternative 1: Return/buy again

If you intended to use your mother's account to buy the album you may try to return the item using iTunes on your computer (Store > My Account...).

In case that you get a refund you can buy the album using the other Apple ID.



Alternative 2: iCloud Family Sharing

If you set up Family Sharing you are able to download purchases made by other members of your family that are a part of Family Sharing.