Flow React HOC typing (without HOC)

I need to type HOC for my component (and that was asked millions of times). But I need to do something opposite to the typical withSomething injection. I need to add an extra property to my outer component and pass all other (but unknown) properties to the inner component:

// @flow

import * as React from 'react'

// That's an example of a standard component doing nothing
type Props = {|  str: string,  num: number |}
const Hello = ({ str, num }: Props): React.Node => {
  console.log(str, num)
  return <div>'Hello'</div>
}

// That's the standard (and working) example of the component with injected prop.
// It's an equivalent of prop currying, I set str prop to some default value
type InnerInjected = {| str: string |}
const withInnerInject = <P>(
  Component: React.AbstractComponent<$Exact<{ ...P, ...InnerInjected }>>,
): React.AbstractComponent<P> => {
  return (props: P) => {
    return <Component str="aaa" {...props} />
  }
}

const InnerInjectHello = withInnerInject(Hello)


// And here is non-working example. 
export const withOuterInject = <P>(
  Component: React.AbstractComponent<P>,
): React.AbstractComponent<P> => {
  return (props: P) => {
    // I need to pass the bool (or some other variable) to my component to perform 
    // some action with it based on its value and return the standard component with all
    // that component properties that I don't know yet.
    const { bool, ...rest } = props
    return <Component {...rest} />
  }
}

const OuterInjectHello = withOuterInject(Hello)

const Example = (): React.Node => {
  return (
    <>
      {/* Both num and str props are set as intended */}
      <Hello num={25} str="something" >
      {/* str is injected with value of 'aaa' */}
      <InnerInjectHello num={25} />
      {/* Works, but typing is wrong */}
      <OuterInjectHello str="aa" num={25} bool />
    </>
  )
}

I tried several $Diff<> and $Rest<> approaches but they simply don’t work with generics.