(In reply to comment #0)
> I don't like the double "of" in the message.
> 
> -X has added an approval of subtask #YYY of task #ZZZZZZ
> +X has added an approval for subtask #YYY of task #ZZZZZZ

"added an approval for subtask" wouldn't be grammatically correct.
The only alternative I could think of is

X has given an approval to subtask #YYY of task #ZZZZZZ

but what about revocations?

(В ответ на комментарий №1)
> X has given an approval to subtask #YYY of task #ZZZZZZ
> 
> but what about revocations?

X has revoked/cancelled an approval to subtask #YYY of task #ZZZZZZ?

(In reply to Олег Соловьев from comment #2)
> (В ответ на комментарий №1)
> > X has given an approval to subtask #YYY of task #ZZZZZZ
> > 
> > but what about revocations?
> 
> X has revoked/cancelled an approval to subtask #YYY of task #ZZZZZZ?

You can "give to", but you cannot "revoke to".  This would have to be smth like
"X has revoked the approval that was given to subtask #YYY of task #ZZZZZZ"
which is somewhat lengthy.

(In reply to Dmitry V. Levin from comment #3)
> (In reply to Олег Соловьев from comment #2)
> > (В ответ на комментарий №1)
> > > X has given an approval to subtask #YYY of task #ZZZZZZ
> > > 
> > > but what about revocations?
> > 
> > X has revoked/cancelled an approval to subtask #YYY of task #ZZZZZZ?
> 
> You can "give to", but you cannot "revoke to".  This would have to be smth
> like
> "X has revoked the approval that was given to subtask #YYY of task #ZZZZZZ"
> which is somewhat lengthy.

"X has revoked the approval from subtask #YYY of task #ZZZZZZ"

If it is still lengthy we can write something like "task #ZZZZZZ:YYY"

(Ответ для Олег Соловьев на комментарий #0)
> I don't like the double "of" in the message.
> 
> -X has added an approval of subtask #YYY of task #ZZZZZZ
> +X has added an approval for subtask #YYY of task #ZZZZZZ

Personally, I don't see anything awful in a sequence of "of" in a language such as English (contrary to Russian), which has lost most inflection (cases), similarly to French. (Modern English grammar resulted from the pressure of French, which was spoken by the noble men after the Norman conquest.) Compare a sequence of "de" in French, which raises no stylistic questions -- https://fr.wikipedia.org/wiki/RPM_Package_Manager :

RPM est un système de gestion de paquets de logiciels
RPM is  a  system  of management of packages of software

* * *

As for the prepositions that "approval" can govern, I found some more examples, showing the use of "for", "of", and "on":

https://en.wiktionary.org/wiki/approval#Noun :

    I need to get an approval on this purchase order.

https://www.oxfordlearnersdictionaries.com/definition/english/approval?q=approval :

     approval of something The government is seeking approval of its plans.
    The proposal is subject to approval by the shareholders (= they need to agree to it).

    approval for something from somebody They required/received approval for the proposal from the shareholders.

    approval for something He won approval for his project.

    approval from somebody He left without obtaining the necessary approval from the authorities.
    She expects to gain final approval from the council.

Extra Examples

    The committee is expected to recommend approval of the new drug.
    The government has now given its approval for the new examinations.
    The scheme did not meet unqualified approval.
    We already have approval for six products.
    We have submitted a design for approval.
    You may not decorate the flat without the landlord's approval.
    Alterations to the hotel must have planning approval.
    The measure would require the approval of the European Parliament.
    The treaty still required approval by the Senate.
    The winning photo will be published in the magazine, subject to the Editor's approval.