Hi ,
1.Just add the domain name @student.com on the accepted domain list as authoritative.
2.Then make sure all the of students contacts in active directory to be mail enabled with external email address with googlemail domain suffix.
3.Then move all the students mail enabled contacts to a separate OU.
4.Then create a email address policy and apply it to the ou to have the new email address with primary smtp address with the domain suffix @student.com.
On the above step please make sure the option "Automatically update email addresses based on the email address policy applied to this recipient" is checked for all the contacts to have their email address to get automatically updated.
5.Then finally all your staffs can able to see their students email address which ends with @student.com as a primary one and if they trigger en emails to that contact , automatically those emails will get delivered to the Google mailbox.
Please reply me if anything is unclear.