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I edited this question, since the original (or current one, revised by ColleenV) post has this sentence.

For instance, in “She told me that she has a gun”,

I edited this sentence to

For instance, in “She told me that she had a gun”,

because I was taught in my country, that if the main verb is the past sentence, the verbs after the "that clause" follows the same time tense of the main clause "generally" (if the verb in the main clause is the present tense, either the past tense can apply after the that-clause, or if the verb in the main clause is the past tense, either the past tense or the perfect past can apply (in this case, it is "She told me")).

But ColleenV advised me "Dude, you are not correct, has is O.K" (frankly saying).

But according to this English site (in English), the idea is same with mine too, accordingly,

Some verbs (generally those connected with reporting) can be followed by an indirect object (underlined) plus a that-clause acting as the direct object:

Examples

He told us that it would take a long time.

She convinced me I was wrong.

(as it is based on the premise that the verb "convince" is under the same category with the verb "tell", which is the reporting verb.

So, which one is correct? Is it mine or Colleen's advice?

Thank you for your tip no matter which is correct in advance.

Thank you very much for your answer typleA.

Since, excuse me, I am not a native speaker, it would take a lot of time to "discuss" this issue if I have to make a through research in English. So excuse me to quote a source in my own language.

The above site is listing the patterns when the agreement of the time sequence would not apply. And one case is listed accordingly, it says,

(2)
現在なお続く状態や習慣を表す場合

Translated

(2) When the case in question is still continuing even now or in case when it it is habitual. (So literally, same with your answer.)

The station master told me that the first train starts at five.
　
He said that he rises early every morning.

ただし習慣的な事柄でも現在どうなっているかを考慮しない場合には過去形にすることができます。

Translated

However, the case in question does not need to address if the situation is still going on or what is happening now on it, you can have the verb in that-clause as the past tense.

He said that he rose early every morning.

Thanks!

Both are perfectly correct. The meanings are not exactly the same, and you would use one or the other in different situations.

She told me she has a gun.

Use this form if the situation is ongoing in the present. If a police officer intervened, you might say this to them. The implication is that she still has the gun at the time of your statement, but her telling you happened in the past.

She told me she had a gun.

She doesn't have the gun anymore, or the event as a whole happened in the past. You might say this to the police if asked sometime later, or in court.

@ColleenV was right to roll back your edit as you changed the meaning of a sentence in the post without good reason. It was not a mere typo (and even then you should be careful when editing others' posts and don't do this lightly, but this would be a better discussion for Meta.)