Your partner has a right to take Shared Parental Leave and must not be subjected to any detriment because he seeks to use this right. His employer needs to be reminded of this and that if he treats him differently from a woman taking time off to look after a baby, this is also likely to be unlawful sex discrimination.
Your partner might have a more constructive conversation with his employer about how to manage his Shared Parental Leave if there is a better understanding of the new right. Helpful guidance for employers is available from Acas (PDF, 786KB) and the Department for Business, Innovation & Skills (PDF, 412KB).
Your partner should also look at the resources on the SPLASH web portal, a practical guide for employees and employers, built by a group of charities and legal experts to explain the shared parental leave regime.