Currently, you can't transfer a token directly on the Async site. However, you can easily do this using OpenSea or SuperRare.
How to burn or transfer a token on OpenSea
Step 1
Go to OpenSea and log in with the same ETH address you use on Async.
Note: if you use the email sign-up on Async, you will not be able to complete this action on OpenSea.
Step 2
Hover over the profile icon in the top right corner and select 'My Profile' from the dropdown menu.

Step 3
Click on the token you want to transfer into your collection to open the token's page. On this page, you'll see a paper plane icon in the upper right. Click this.

Step 4
On the next page, you will be required to provide the address where you would like to transfer the token.
Note: If you want to burn the piece you can send it to this address:
0x000000000000000000000000000000000000dEaD
This address isn't owned by anyone so no one can access any tokens sent here - that's why this is commonly used for burning tokens.
How to burn or transfer a token on SuperRare
Step 1
Go to SuperRare and log in with the same ETH address you use on Async.
Note: if you use the email sign-up on Async, you will not be able to complete this action on SuperRare.
Step 2
Hover over the profile icon in the top right corner and select 'Profile' from the dropdown menu.

Step 3
On the profile page, ensure you have the 'Collections' tab selected.

Find the token you want to transfer to your collection. Click the three vertical dots and select 'Transfer'.

Step 4
Clicking 'Transfer' will open this screen. should bring you to this screen. You will now be required to provide the address where you would like to transfer the token.
