Any typescript chads able know if it's possible to map a type to another type w generics

const A = {
  s: string,
}
const AMapsTo = {
  someAProperty: string,
}
const B = {
  n: number,
}
const BMapsTo = {
  someBProperty: string,
}
const a: A = {s: "cool"}
const b: B = {n: 0}
const aMaps: AMapsTo = {someAProperty: "cool"}
const bMap: BMapsTo = {someBProperty: "cool"}

const myMapping = [[a, aMaps], [b, bMaps]]

// Doesn't have to look exactly like this
function myBuilderFunction(myMapping) {
  // ...
  // Some type safe function. When called with A the type is inferred as AMapsTo
  return (preMappingValue: SomeType)=>SomeTypeMapsTo
}

const fn = myBuilderFunction(myMapping);

fn(a) // Typed as AMapsTo