It will depend on what is asked on the job application form. Generally employers will not have the right to ask about previous cons unless the employment involves dealing directly with 'vulnerable people' - amongst these such people as children, disabled, old and... wait for it... ex-offenders. This means a real 'hands on' dealing with them, not just selling them things from a counter or just speaking to them on the phone..... the situation is fluid, but if not asked about any previous, then your boyfriend has a total right never to refer to any.