Send a connected account to a linked company, the family's personal side, or not used

Firm-side family relationships only. Select the firm with x-organization-id. Owners, Admins and Staff Admins access all firm families; Staff Members need independent family assignment. Company access does not grant family access. OAuth requires the broad mcp grant, not a narrow banking scope; API keys retain ordinary agent permission scopes. No accounting organizations, portal grants, bank changes, invitations or charges are created. Writes require ordinary firm write entitlement. Cross-firm and inaccessible IDs return 404. Exception: this operation changes bank routing. Each account goes to exactly one place. Moving to another company brings the account's unposted rows, including rows whose posting was undone, unless moveHistory is false; moved rows lose their old company's coding. Posted or reconciled rows, and rows tied to that company's client questions, checks or payments, stay in the old company and never block the move. Sending to personal requires the company's unposted rows to be posted or excluded first (409 account_has_unposted_rows). A new register that looks like an existing one returns 409 possible_existing_register with candidates; resend with confirmNewRegister true to create it anyway. Requires banking permission.