Most of what I was going to write about this prophecy has already been stated in a video.
The main facts surrounding this prophecy are essentially uncontested. Branham did die suddenly in the specified time frame. He is on record for false teaching.
Hagin repeated his recollection of his prophecy in print and on a few occasions during public speaking. He can be considered an honest source; he was a veteran minister not known for lying or deception.
Mrs. Freda Lindsay, late wife of the late Gordon Lindsay, can also be considered an honest person. There is no obvious reason to doubt her story. Her husband had known Branham since the 1940s and had in fact started a magazine, The Voice of Healing, to promote his healing ministry, and written his biography, William Branham: A Man Sent From God, a key book used in the promotion of his ministry.
Lindsay would very likely have been aware of any complaints against and any new false teaching introduced by Branham in the 1960s. He also, because of their friendship, would have had access to Branham to bring warning or correction if needed.
There is not much indication Hagin and Branham had a friendship. If they had, you would have expected Hagin to say he personally confronted Branham and told him he would die. Hagin, however, was ironically featured by Lindsay in one issue of The Voice of Healing and some of his ministry was promoted in the magazine. But it seems more likely they just happened to have independent healing ministries at the same time during the healing revival, and did not advertise campaigns working together. (Most evangelists back then had independent campaigns.)