transfer Bitcoin without synchronizing Bitcoin core
The good (or bad) news is that your friends hasn't sent you any bitcoins to address 13BuBwcQM2WwedYzqkccovjYYPKBAc6RWE yet so ask him not to do so until you configure your account to blockchain.info or another online wallet. 

Before you proceed with deleting your local wallet, keep the wallet.dat file so you will be able to restore it later on if needed.