“Built-in” or “In-built”

Actually, this is written "inbuilt" and not "in-built".
It is an old (1923) chiefly British synonym for built-in.

• Constructed as part of a larger unit; not detachable: a built-in cabinet.
• Forming a permanent or essential element or quality: a built-in escape clause

Example:

"Of course, even the most able driver in the most dynamically competent car can sometimes find his or herself in a situation where a collision is inevitable, so with this in mind the Spark was designed with high levels of passive safety inbuilt from the outset."

—Automotive Headlines

This is one of those ones where Google, whatever faults it might have, does tell you something significant:

"built-in extractor fan"      643,000 results
"in-built extractor fan"          137 results

Subjectively, from the first ten results, it looks like the "in-built" hits are largely from the UK. I've never even heard of an "in-built extractor fan".

Just at a guess I would think that "in-built" would go with "ability", so I tried it on Google:

"built-in ability"  216,000 results
"in-built ability"   75,500 results