How can they present it? Through witnesses. The same witnesses who testified in the first trial, no?
No. It was written that way in the jury instructions.
To give a little background, the two charges in the new trial were barely mentioned at all during the first trial. The focus of the first trial was on the other three counts, which alleged that he misused public money. Until the last day of the trial, when the judge changed the rules, a conviction on counts 3 and 5 (the two he was convicted of) was not allowed without a conviction on one of the other counts. So instead of confusing the jury, the defense focused on counts 1, 2, and 4, which was the primary focus of the entire case. But after they rested their case, the judge disconnected counts 3 and 5 from 1, 2, and 4, and that is how he was able to be convicted.
Now, the entire case is focused on Counts 3 and 5, so a lot more is naturally being discussed about them.
(Count 3 is financial facilitation, which means that the defendant used the proceeds of one crime to commit another. During the first trial, the first crime WAS the other counts, until the judge allowed them to convict on it without a conviction on the other counts. Since he was vindicated on the other counts, the prosecution has repeatedly shifted their narrative as to what the first crime is.)