" I have alert that exec a job but I don't know how to pass the alert message to the job."

The documentation regarding alert tokens ( variables ) is well hidden and described under "sp_add_jobstep (Transact-SQL) " An example of a alert token is

$(A-DBN)

Database name. If the job is run by an alert, the database name value automatically replaces this token in the job step.

By default, alert token access is disabled but can be enabled by configuring the SQL Server Agent. See BOL "Using Tokens in Job Steps"