When start COBRA?

Our insurance policy states that we pay the full month's premium at the 1st of the month and that the employees are covered through the end of the month in which they terminate. At the end of FMLA, they are given the option of elect COBRA.
My question is, when an ee is out on FMLA and the 12 weeks of FMLA ends prior to the end of the month, and they elect COBRA, would it be correct to not begin their COBRA payment until the 1st of the next month?
My question is, when an ee is out on FMLA and the 12 weeks of FMLA ends prior to the end of the month, and they elect COBRA, would it be correct to not begin their COBRA payment until the 1st of the next month?
Comments
In our case, the employee who has not returned on the appointed day is terminated unless they apply for an extension of FMLA and pay the premium up front cost. If not back by the approved extension date, whatever the date of termination is, is also the date for the determination of starting date for COBRA. Termination date is the beginning of COBRA in all cases regardless of who paid the premium or when it was paid. The insurance company will credit the over payment back to us next month and expect the individual to communicate with the insurance carrier and pay for all personal premium expenses from the termination date forward.
I hope this helps.
PORK
Some insurance companies might continue it through to the end of the last month for administration purposes, but your legal obligation ends 18 months after the term date.