Choose a second background to complement this one, reflecting your upbringing: you gain its Background Feature in addition to your Birthright.  You can also choose either this background's proficiencies or those given by your adoptive background.  Any equipment (aside from your inheritance), other items, and features all follow the rules as stated by your adoptive background.

Birthright:

Choose or randomly determine your Birthright from among the possibilities in the table below. Work with your Dungeon Master to come up with details: Why is your Birthright important, if at all, and what is its full story?  Did your adoptive parents ever reveal it and/or give it to you?  You might prefer for the DM to invent some of these details as part of the game, allowing you to learn more about your Birthright as your character does.

The Dungeon Master is free to use your Birthright as a story hook, sending you on quests to learn more about its history or true nature, or confronting you with foes who want to claim it for themselves or prevent you from learning what you seek. The DM also determines the properties of your Birthright and how they figure into the item’s history and importance. For instance, the object might be a minor magic item, or one that begins with a modest ability and increases in potency with the passage of time. Or, the true nature of your inheritance might not be apparent at first and is revealed only when certain conditions are met.  It might even simply be a charm of love left by parents that understood they could not give you the life they felt you deserved.