Wizard / Improved familiar skill bonus?

[Aroth Khashar]

Does a wizard with an "improved familiar" still get the skill bonus their original familiar granted them?

[Lucy_Valentine]

No. Because they don't have the original familiar.

[Agénor]

No, they do not.
Improved Familiar allows one to replace one's Familiar by choosing from a wider list. What Familiar the Wizard had before taking this feat has no bearing on the perks provided by the new Familiar to the Wizard.

[Name Violation]

I thought if they chose the "template upgrade" (fiendish, celestial) that those still granted the skill bonus.

I may be completely wrong tho

Improved familiars otherwise use the rules for regular familiars, with two exceptions: if the creature’s type is something other than animal, its type does not change; and improved familiars do not gain the ability to speak with other creatures of their kind (although many of them already have the ability to communicate).

It doesn't say the skill bonus doesn't apply, just that it doesn't gain speak with animals