It is not uncommon, when leaving one barn and going to another to pay board at two places for one month.
If you can in good conscious say that this horse is yours then pack this horse and your other horse onto the trailer. While the trailer leaves hand the barn owner your 30 days notice with a check for board for both horses for that 30 days.
Notice usually starts on the day your board is due. If your board is due on the first of the month then you give notice the first of the month (or shortly before) for the next month.
ETA - What JDI said above (while I was typing).