This is correct.
The way to think about it is 52 weeks leave be that maternity, shared parental, adoption etc. Plus two weeks paternity leave.
39 weeks of which are paid SMP/SAP/ShPP. Plus 2 weeks SPP.
The mother must take at least the first two weeks after giving birth. The partner gets two weeks paternity leave. Normally the two weeks are the same.
One benefit of ShPL is both partners get 20 days SPLIT I.e. 40 days jointly.
With SPL each parent can take leave in 3 blocks.
An option is the Mother takes 26 weeks paid leave but after the 2 mandatory weeks converts to SPL. The Mother gives up the remaining 13 weeks paid and splits the 13 weeks unpaid I.e. 6 and 7 weeks. During the 6 or 7 weeks unpaid they can work SPLIT days.
The partner takes the two weeks paternity leave at the start. They then get 13 weeks paid (so 15 weeks paid) plus 6 or 7 weeks unpaid. Again working SPLIT days.
During the unpaid weeks aim to work 2 split days. This is feasible as the other partner is at home so no child care costs. Plus it allows each parent 1 on 1 time with their DC.
Break the paid into blocks and intersperse with blocks of unpaid where each partner works some SPLIT days. If you work it right so in some pay periods you get only unpaid leave plus paid SPLIT days you should get a tax rebate maximising income.
Added to this you both accrue annual leave and this can be used to extend paid leave.
My advice draw a table with the weeks in the first column, Mothers leave and pay in the next two columns and Partners leave and pay in columns 4 and 5. Then both run it past your HR.