Shared ownership properties don't necessary have so many more restrictions than normal mortgages or lease agreements. They have a few but in most cases these restrictions are understandable.
Can your partner move into your shared ownership?
Yes but you must ensure you inform your local council if you want your partner to be liable for the council tax and you must also inform your shared ownership provider.
You should ensure your partner does not pay for the mortgage, rent or anything that has to do with the property if not they may be able to prove in court that they had some interest in the property.
In some cases, the mortgage lender might require any cohabitants to sign an exclusion agreement stating that they are not a party to the mortgage.