You'll need to keep the inputs to the credential so you can re-create it in the backend handler.
This is either an authorization code, or the access token and refresh token that you got in exchange for the authorization code. They're all strings so should serialize readily.
If all that sounds unfamiliar, I'd be curious to understand how you got the Credential in the first place. Links to useful documentation below:
Notably, sample code in that last link specifically includes a method that you're expected to implement to squirrel away the access/refresh tokens:
/**
* Retrieved stored credentials for the provided user ID.
*
* @param userId User's ID.
* @return Stored Credential if found, {@code null} otherwise.
*/
static Credential getStoredCredentials(String userId) {
// TODO: Implement this method to work with your database. Instantiate a new
// Credential instance with stored accessToken and refreshToken.
throw new UnsupportedOperationException();
}