Having decision making power over someone's assets
The answer you already found is the most accurate imo.
You have the power of disposal (or power of disposition) over the assets etc.
power of disposal — An expression used in reference to the power of one other than the owner of property to dispose of it by will. See power of appointment; power of sale …
Ballentine's law dictionary
Dispose doesn't just mean to get rid of something. In ordinary language, too, if you have something at your disposal, it means you can do as you please with it -- in the sense of controlling. Disposal -- sense 4. from Dictionary
power or right to dispose of a thing; control: left at his disposal.
dispose (entry 5 from Dictionary)
to arrange or decide matters: to do as God disposes.
Linguee is a good translator site for German-English. You can find lots of translations in context.
Here's a sample translation of the verb 'verfügen' used in the sense you are looking for. From Deutche Bank.
[...] regarding the SG Postbank Shares, and (iv) SG will be free to dispose of the SG Postbank Shares at is own discretion at any time.
[...] Weisungsrechte gegenüber SG zustehen und (iv) SG nach eigenem Belieben jederzeit über die SG-Postbank-Aktien verfügen kann.
Or here from wintershall.mobi:
[...] buy, sell, exchange or otherwise dispose of, or issue, or any solicitation of any offer to sell or issue, exchange or otherwise dispose of, buy or subscribe for, any securities, [...]
[...] Kauf, den Verkauf, den Tausch, die Zeichnung oder eine anderweitige Verfügung von Wertpapieren und stellt mit Bezug auf solche Wertpapiere auch keine investitionsbezogene, [...]
Linguee also introduces authority to dispose of as the right of disposal.
In sum you could use power of disposal, power of disposition, right of disposal/disposition or authority to dispose of and as a verb dispose (of).
*Edit. In general I understand your wariness of translating mistakes getting spread by mistranslation online, but in this case I figure it's the correct English usage. If you google e.g "right of disposal" you will find a lot of non-translated English entries using it in 'natural' contexts. Here's one:
Sale of Goods Act 1979 [England]
- Reservation of right of disposal 113
(1) Where there is a contract for the sale of specific goods or where goods are subsequently appropriated to the contract, the seller may, by the terms of the contract or appropriation, reserve the right of disposal of the goods until certain conditions are fulfilled; and in such a case, notwithstanding the delivery of the goods to the buyer, or to the carrier or other bailee or custodier for the purpose of transmission to the buyer, the property in the goods does not pass to the buyer until the conditions imposed by the seller are fulfilled.
Executor Lexico/Oxford:
1 A person or institution appointed by a testator to carry out the terms of their will.
2 A person who produces something or puts something into effect.
Trustee Lexico/Oxford:
An individual person or member of a board given control or powers of administration of property in trust with a legal obligation to administer it solely for the purposes specified.