The front suspension unit (spring based are anything else) lower end of the Birdy is bolted to the moving part of the fork.

But the upper end isn't bolted, its only slightly nested in the fixed part of the fork and held by a single hook.

There is no rigid link between the suspension unit and the fixed/suspended part of the fork that could provide any rigidity improvement of the fork.

The lateral rigidity of the fork comes from the two axles between the moving part and fixed part of the fork located at the bottom right and left side of the fork. Because the fork is quite wide at this place, it provides and excellent lateral rigidity.

Another problem with third party Birdy front suspension unit is that the hook has a curved shape meant to fit to a spring. It isn't adapted for the square shaped groove of third party front suspension. As consequence, the front suspension is not firmly held by the hook, there is some play that you feel when there are rebounds.