Swapping BNB from BEP2 (Binance Chain) to BEP20 (Smart Chain) using Binance Chain Extension Wallet
Binance Chain Extension Wallet is the official browser extension wallet from Binance and it offers a convenient way to swap assets from BEP2 to BEP20 between your accounts.
Once you have BNB as BEP2 in your Binance Chain Extension Wallet, you can swap it to Smart Chain (aka Binance Smart Chain) within the wallet.
Login to Binance Chain Extension Wallet. Make sure the network selector at the top says "Binance Chain Network" like in this screenshot:
Click "Send" button
On the next screen, click into the Address field
A drop-down saying "Transfer between my accounts" will appear underneath the Address field. Click on that drop down and select the item that says "Binance Smart Chain Network" and shows your Binance Smart Chain address.
Enter the amount you want to send or click "Max" to send all BNB and click "Send.
After you click "Send", the wallet will ask you to confirm the transaction. On the confirmation screen, make sure that "From" section says "Binance Chain Network" and "To" section says "Binance Smart Chain Network" like on the following screenshot.
Hit "Send" to confirm the transaction and wait 2-3 minutes for the network to prcess it. To see your BNB in your Binance Smart Chain account, click the network drop down at the top of the wallet screen and select Binance Smart Chain.
You will see your account balances on Binance Smart Chain