"Peter laid the whole matter before them. He related his experience in regard to the vision and pleaded that it admonished him to observe no longer the ceremonial distinction of circumcision and uncircumcision, nor to look upon the Gentiles as unclean. He told them of the command given him to go to the Gentiles, of the coming of the messengers, of his journey to Caesarea, and of the meeting with Cornelius. He recounted the substance of his interview with the centurion, in which the latter had told him of the vision by which he had been directed to send for Peter. AA 141.2"
"On the morrow, as they went on their journey, and drew nigh unto the city, Peter went up upon the housetop to pray about the sixth hour: And he became very hungry, and would have eaten: but while they made ready, he fell into a trance, And saw heaven opened, and a certain vessel descending unto him, as it had been a great sheet knit at the four corners, and let down to the earth: Wherein were all manner of fourfooted beasts of the earth, and wild beasts, and creeping things, and fowls of the air. And there came a voice to him, Rise, Peter; kill, and eat. But Peter said, Not so, Lord; for I have never eaten any thing that is common or unclean. And the voice spake unto him again the second time, What God hath cleansed, that call not thou common. This was done thrice: and the vessel was received up again into heaven. Now while Peter doubted in himself what this vision which he had seen should mean, behold, the men which were sent from Cornelius had made enquiry for Simon’s house, and stood before the gate, And called, and asked whether Simon, which was surnamed Peter, were lodged there. While Peter thought on the vision, the Spirit said unto him, Behold, three men seek thee. Arise therefore, and get thee down, and go with them, doubting nothing: for I have sent them. Then Peter went down to the men which were sent unto him from Cornelius; and said, Behold, I am he whom ye seek: what is the cause wherefore ye are come? And they said, Cornelius the centurion, a just man, and one that feareth God, and of good report among all the nation of the Jews, was warned from God by an holy angel to send for thee into his house, and to hear words of thee. Then called he them in, and lodged them. And on the morrow Peter went away with them, and certain brethren from Joppa accompanied him. And the morrow after they entered into Cesarea. And Cornelius waited for them, and had called together his kinsmen and near friends. And as Peter was coming in, Cornelius met him, and fell down at his feet, and worshipped him. But Peter took him up, saying, Stand up; I myself also am a man. And as he talked with him, he went in, and found many that were come together. And he said unto them, Ye know how that it is an unlawful thing for a man that is a Jew to keep company, or come unto one of another nation; but God hath shewed me that I should not call any man common or unclean."
The EGW passage summarizes Peter's account of his vision and interaction with Cornelius, which is directly described in Acts 10:9-48. While not a direct quote, it accurately reflects the events and themes of the biblical narrative.
"“As I began to speak,” he said, in relating his experience, “the Holy Ghost fell on them, as on us at the beginning. Then remembered I the word of the Lord, how that He said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost. Forasmuch then as God gave them the like gift as He did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?” AA 141.3"
"And as I began to speak, the Holy Ghost fell on them, as on us at the beginning. Then remembered I the word of the Lord, how that he said, John indeed baptized with water; but ye shall be baptized with the Holy Ghost. Forasmuch then as God gave them the like gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?"
This is a direct quote from Acts 11:15-17.