Can lightweight wallet users exchange money? Instead of downloading full block chain, lightweight (SPV) users only download blockheaders of the blockchain.

This makes SPV users to check if transactions are confirmed or not. However, can SPV users also exchange money without being full nodes? That is, can they create a transaction and send it to nodes?
Instead of downloading full block chain, lightweight (SPV) users only download blockheaders of the blockchain.


Not all thin client are doing it. 


  Can the *SPV clients create a transaction and send it to nodes?


yes, they can create a transaction. The example of thin client is Electrum wallet.

Electrum fetches blockchain information from Electrum servers, bitcoin nodes that index the blockchain by address. Electrum performs Simple Payment Verification to check the transactions returned by servers. For this, it fetches blokchain headers from about 10 random servers. 


* SPV - Here is lightweight client