No Your VAT on Dept B will come. When you render services & Only services then there cannot be use of any material, but when you use some material for rendering services then
1) Either that material trfd will be shown as material sold to the Customer Srvc Recvr coz there is the transfer of Rights in the material along with the SRvcs, even if there is no material seen seperately but Mtrl is an Integral part in completion of the Srvcs. ( Refer Provisions of JOB WORK & Taxation of that under VAT & your point will get cleared)
2) If its only srvcs if you claim that then you can also come under Works contract ( Refer WCT Act under VAT & Srvc TAx)
Refer JOb work & Works Contract Tax Prov under VAT & Srvc Tax & your issue will get cleared. There is nothing as Brain Teaser inthis situation. It is a clear case of J/W or WCT based on actual situation for Dept B who pays Tax there on, Withour any Onput credit as it has been trf from Dept A without VAT.