Divorced with the Survivor Benefit Plan

I'm retired military and I have a couple years of alimony to go. My alimony comes out of my retired pay, and right now it's set up where it's a little less than the full alimony amount because my divorce decree says we share the cost of the SBP. But when my alimony payment period is over, how will my ex-spouse pay their half of the monthly SBP payment? I didn't have an amicable divorce so I feel it's going to be a challenge to get a fair split when it comes to funding their half of the SBP monthly payment. (My SBP monthly payment is currently $211, so that's $105.50 a month I will need to figure out how to get back. Not a remarkable amount, but it will add up over a lifetime.)

Does anyone else share the cost of the SBP with a divorced spouse? How do they pay for their half? My ex-spouse also gets part of my retirement, so maybe it will be deducted from that?

Thanks for any info you can share!