If the Switch A already correctly routes all defined VLANs (VLAN 10, 20 and 30) you just need to permit all those VLANs on both your two Switches uplinks (Uplink 1: Switch A Port B1 <--> Switch B Port 45 and Uplink 2: Switch A Port B2 <--> Switch C Port 45) so tagged traffic that belongs to VLANs 10 and 20 will be permitted between Switch B and C through Switch A by means of its two uplinks.
The same for tagged traffic that belongs to VLAN 30, it will permitted between Switch C and B always through Switch A by means of its two uplinks.
That way all VLANs speak with all VLANs through routing Switch A.
Basically you should permit involved VLANs on each involved ports (Ports B1 and B2 on Switch A, Port 45 on Switch B and Port 45 on Switch C).
I actually suppose your involved ports are yet of Type Trunk and yet permit actually (and respectively) only VLANs 10 and 20 on Switch A <--> B uplink and only VLAN 30 on Switch A <--> C uplink...this to say that, actually, VLANs traffic flows correctly between Switch B and A, from Switch C and A but not between Switch B and C through Switch C.