what happens if a miner include a transaction already exists in another block? Suppose that I have a Transaction A. (txA)
I send my txA to bitcoin network and full node validate it and put in Mempool and starts to broadcasting it.

A Miner A connect to a fullnode to create a candidate block and wins the POW. In this block there is my txA

A miners B create another block with all different transactions except to my txA.

If block A and block B have the same previous block Hash it's a fork,and if the chain of block A wins, all transaction of block B return to mempool.

But if B Has the previous block hash of A ?
After create a block there is another check of all transactions?
When TxA is in mempool it's unconfirmed when become confirmed?
It can only exist in one block.  That is why it is safer to wait for 2-6 confirmations before accepting a large transaction.  

So to answer the title of your post - a miner can't include a transaction which exists on another block in the same chain since it would not be a valid block.