M in HK after X2 visa's expiration

Hello,
I am Italian and I just got here in Italy a X2 (90 days). In April I will go to Beijing to attend a Chinese language course at BLCU. In the end of June 2014 the course will finishing and it will expire. After the school experience, I would like to remain in China other 3 months due to I already found a Chinese Company for an internship. If in June I will come to Hong Kong, can I ask for a 90 days M (with the Company invitation letter and all the required documents)?

Thank you!