when UE capability enquiry happens during Inter-RAT handover and please tell message flow?

Answer 1

During Initial attach procedure before AS security establishment eNodeB will enquire about UE capability by sending UECapabilityEnquiry in respond to that UE will send UECapabilityInformation which will carry Eutra capabilities,Geran capabilities,Layer specific capabilities like whether UE supports DRX/SPS/TPC or how many ROHC profiles it supports or whether it supports CA or not,etc.
So according to me UEcapabilityEnquiry is mandatory message during initial attach procedure,same capability information will be forwarded to other eNodeB during handover procedure(intra rat,inter frequency,intra frequency).

Answer 2

As far as I know, eNodeB does "UE capability enquiry" as part of "Initial Context Setup Procedure" .
The "UE Capability Enquiry Procedure" is an optional procedure . An eNodeB triggers this procedure if UE capability is not received in Initial Context Setup Request message.

UE Capability Enquiry procedure is necessary to take handover decision from LTE to other RATs .