“My Lord, I have good news on that score. I have—with difficulty, and after great effort—succeeded in placing an Imperius Curse upon Pius Thicknesse.” Many of those sitting around Yaxley looked impressed; his neighbor, Dolohov, a man with a long, twisted face, clapped him on the back. “It is a start,” said Voldemort. “But Thicknesse is only one man. Scrimgeour must be surrounded by our people before I act. One failed attempt on the Minister’s life will set me back a long way.” (DH, Chapter 1)
and
“All right, all right, we’ll have time for a cozy catch-up later,” roared Moody over the hubbub, and silence fell in the kitchen. Moody dropped his sacks at his feet and turned to Harry, “As Dedalus probably told you, we had to abandon Plan A. Pius Thicknesse has gone over, which gives us a big problem. (DH, Chapter 4)
Now, the battle of Seven Potters occurred on 27 July, 1997.
OTOH, the Ministry fell on 1 August, 1997 (Bill and Fleur's wedding).
If the Order knew about Thicknesse having "gone over" 4 days in advance, why didn't they warn Minister of Magic Scrimgeour in time so he could de-Imperius Thicknesse and/or take some additional measures to prevent the Ministry from falling 4 days later?
I prefer canon info, if available.
But Thicknesse is only one man. Perhaps they were hoping they would get more information beyond knowing that Thicknesse had gone over. Like what other pieces where going to be put in place, and when the attack on the Scrimgeour would happen. Telling Scrimgeour about the state of a single pawn wouldn't be very much help if it means you no longer get to see the state of all the other pieces on the chessboard. Surely he would have already expected that there were agents trying to get to him.