How did Peter learn of Anania's deception?

[TonyChanYT]

The nascent church experienced quite a few miracles. The episode of Ananias and Sapphira was one of them. Acts 5:

1But a man named Ananias, with his wife Sapphira, sold a piece of property, 2and with his wife’s knowledge he kept back for himself some of the proceeds and brought only a part of it and laid it at the apostles’ feet. 3But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit and to keep back for yourself part of the proceeds of the land?

Peter cited the Holy Spirit. I think Peter received a specific revelation directly from the Spirit.

4While it remained unsold, did it not remain your own? And after it was sold, was it not at your disposal? Why is it that you have contrived this deed in your heart? You have not lied to man but to God.” 5When Ananias heard these words, he fell down and breathed his last.

God terminated Anaias supernaturally.

And great fear came upon all who heard of it. 6The young men rose and wrapped him up and carried him out and buried him.
7After an interval of about three hours his wife came in, not knowing what had happened. 8And Peter said to her, “Tell me whether youa sold the land for so much.” And she said, “Yes, for so much.” 9But Peter said to her, “How is it that you have agreed together to test the Spirit of the Lord? Behold, the feet of those who have buried your husband are at the door, and they will carry you out.” 10Immediately she fell down at his feet and breathed her last.

God terminated Sapphira supernaturally.

When the young men came in they found her dead, and they carried her out and buried her beside her husband. 11And great fear came upon the whole church and upon all who heard of these things.

It was a sequence of three supernatural events, beginning with the Holy Spirit's supernatural revelation to Peter.

Cambridge Bible explained:

We must believe that the Holy Spirit gave Peter knowledge of the deception which Ananias was seeking to practise on the Church, and most likely also of the punishment which should come upon the offender. Otherwise we can hardly account for the calm manner of the Apostle when such a startling judgment was inflicted in an instant.

How did Peter learn of Anania's deception?

The Holy Spirit dwelling in Peter told him and ordered the subsequent executions to teach a lesson to the people in the early church.