Add a "Who invited you?" field when someone joins the team space, linked to the right member in the Downline

When someone joins our team space, I have no way of knowing which of my members invited them.

I would like a field asking the new member who invited them — ideally a dropdown/list of the members in my team space, so they pick the actual person instead of typing a name in free text.

Why it matters: with that answer I can put the new member in the right place in my Downline straight away — linked to the member who actually invited them — instead of asking around or guessing.

Desired behaviour:
• A "who invited you?" question on the team space sign-up, which the leader can turn on and word themselves.
• The new member chooses from a searchable list of members in the team space, not free text.
• The answer is saved on the new member's profile, so they can be matched and placed under that member in the Downline.