English to German Bus/Financial Accounting

Es geht hier immer noch um den Depotstellen- und Dienstleistungsvertrag. Wie würdet ihr hier am besten "in its books" übersetzen? Vielen Dank im Voraus!

Custodianship

Safekeeping of the Assets

The XXX-Company authorises the Bank to open ***in its books*** in the name of the Fund one or more securities and/or cash accounts evidencing any Assets from time to time held by the Bank or its Correspondents on behalf of the Fund.

The Bank shall identify ***in its books*** that the Assets belong to the Fund. Notwithstanding the foregoing, the XXX-Company authorises the Bank to hold the Assets in non-segregated accounts with its Correspondents and to combine the Assets with assets/investments held by the Bank for all its clients.