Thumb Latch Deadbolt Handle Set, 1-3/4" - Product Code 40-057

This appears to be a perfect replacement for the very old, broken thumb latch handle on my storm door (the deadbolt upper latch works fine, but the lower latch no longer engages when you press the thumb control in the handle. They look exactly the same and the measurements match. However, I have one question.

On my current set, the lower interior latch

The lower interior latch (not the upper deadbolt latch controlled by the key) no longer engages when you use the thumb control on the outside or the latch handle on the inside. That is really the only part that needs to be replaced.

My question is this: the current lower interior latch has a small sliding bar that locks the latch tongue in place against the strike plate. Does the lower interior latch on this product have the same feature? If not, is there any 1-3/4" interior latch that does?

I've come across an interior latch with a similar sliding control for a non-keyed deadbolt, but that is not what I'm looking for. I'm looking for something that locks the latch tongue.