The in-use translation has some redundancy in the second sentence, so I edited that to increase the comprehension of the dialog message.

The first sentence of the current translation is good. The second sentence doesn’t take into account that “Do you want to” was omitted in the English microcopy to save space, and uses some words indicating the interrogative case in the beginning of the sentence, but omits an important verb. The sentence is understandable, but is neither grammatically correct nor how a native speaker would say it. A correct version of the current translation would be: آیا می‌خواهید او را به گروه اضافه کرده و به مدیر ارتقاء دهید؟

I used passive verbs to rewrite that translation so as not to exceed the character limit. Please note that using passive tense is not as frowned-upon in Persian copy and microcopy writing as it is in English.

The second issue with the current translation is that it misses the fact that in this case the word ‘they’ is a singular pronoun. The translation uses the pronoun آن‌ها which is the plural form of ‘they’. Persian pronouns are not gendered and as such do not require such workarounds. The singular pronoun او is correct in this instance.

My proposed translation reads: ‘This user is not a member of this channel. Do you want them to be added to the group and promoted to admin?’