This is a little tricky because the answer depends on when you reached state pension age.
If you reached state pension age before 6 April 2016, then your state pension comes in two parts – the basic state pension and the additional state pension. You may have built up entitlement under both or just the basic state pension. The basic state pension cannot be shared. However, the additional state pension can be shared.
If you reached state pension age on or after 6 April 2016, you have a “new” state pension. This can‘t be shared. However, if you benefit from a “protected payment” (this is an extra payment on top of the full state pension), that can be shared.