SSO doesn't for web accelerator between SSO sites #400

here is situation:
SSO server site (A): https
web accelerator(B): https
SSO client site(C): http only
try to open C withing A.
process goes this way: A--https--> B --http-->C
and then C --directly--http--> A
for sure this failed because of http communication
is there any approach to make it work without make C with https?
thank you very much in advance
Denny