I checked the site Sarah suggested to me on the personal construction with the passive voice. I hope someone can help me with my doubts. Maybe the sentences are just not possible.

1) They report that Peter is sending her messages.
Peter is reported to be sending her messages.
2) Peter sent her messages//has sent her messages/had sent her messages.
Peter is reported to have sent her messages.
3) They report that Peter was sending
her messages.
Peter is reported to have been sending her messages.
4) They report they are going to send her messages/will send her messages.
I think it is not possible to use the personal construction in the future. What do you think?

2. If one sentence is to be the passive of the other, then both sentences cannot have "Peter" as the subject.

4. is fine. Why not use the future?

To analyze and determine the validity of the sentences using the personal construction with the passive voice, we can break down each sentence step by step:

1) They report that Peter is sending her messages.
To transform this sentence into the personal construction, we can follow these steps:
- Identify the subject (Peter) and the object (her messages).
- Use the reporting verb "report" as the main verb in the passive voice.
- Combine the subject (Peter), the reporting verb, and the preposition "to be" to form the personal construction.
So, the resulting personal construction would be:
- "Peter is reported to be sending her messages."

2) Peter sent her messages/has sent her messages/had sent her messages.
Using the personal construction for these sentences requires modifications similar to the previous example. We follow these steps:
- Identify the subject (Peter) and the object (her messages).
- Use the corresponding reporting verb ("report" in this case) as the main verb in the passive voice.
- Combine the subject (Peter), the reporting verb, and the preposition "to have" to form the personal construction.
So, the personal constructions for these sentences will be:
- "Peter is reported to have sent her messages."

3) They report that Peter was sending her messages.
Again, we follow the same steps to convert this sentence into the personal construction:
- Identify the subject (Peter) and the object (her messages).
- Use the reporting verb ("report") as the main verb in the passive voice.
- Combine the subject (Peter), the reporting verb, and the preposition "to have been" to form the personal construction.
The resulting personal construction will be:
- "Peter is reported to have been sending her messages."

4) They report they are going to send her messages/will send her messages.
In this case, the personal construction in the future tense is not possible. The personal construction is typically used for past actions or situations. Therefore, we cannot convert these sentences into personal constructions.

To summarize, the correct personal constructions for these sentences are:

1) "Peter is reported to be sending her messages."
2) "Peter is reported to have sent her messages."
3) "Peter is reported to have been sending her messages."

Regarding the fourth sentence, you are correct. It is not possible to use the personal construction in the future tense.