The company would need to obtain an approved LMIA in order for him to qualify for a work permit. The LMIA process is long and expensive for the employer - most employers are unfortunately not willing to go through the process for that reason. As a first step, the employer has to advertise the job for at least a month to prove no Canadian could be found for the role. The employer then has to submit the LMIA application for processing which typically takes 2-4 months and also costs the employer $1K. If the LMIA is approved (not all are), then your boyfriend can apply for a work permit.
So it's possible - but very difficult. Your boyfriend would have to start by finding a job in Canada with an employer who is willing to go through the LMIA process.
