How to grant insert in a table that is in another database on SQL Server 2008 R2?
Indeed what I was looking for (but were unaware of its name) is called cross database ownership chaining.

By reading the article Understanding Cross Database Ownership Chaining in SQL Server  I was able to solve my problem.

As a reference, below is what I did:

Use [DatabaseA]
GO

ALTER DATABASE [DatabaseA]
SET DB_CHAINING ON
GO

Use [DatabaseB]
GO
ALTER DATABASE [DatabaseB]
SET DB_CHAINING ON
GO

EXEC sp_grantdbaccess 'UserB';
GO 

GRANT SELECT, UPDATE on [DatabaseB].[dbo].[TableA] TO [UserB]
GO


Thank you all.