I want to pass Txhash of a livenet Bitcoin transaction to a service created in Testnet bitcoin node. I have been using Bitcore as my client for writing services in nodejs. This is my Bitcoin Client
I'm not sure whether this is the information you're asking for, but Testnet uses a different address format and derives from its own genesis block, therefore all content from the mainnet's blockchain is incompatible with testnet. Mainnet transactions are incompatible with testnet.