React - How to pass props to a component passed as prop

You can achieve that by using React.cloneElement.

Like this:

class CustomForm extends React.Component {
  ...
  render() {
    return (
      <div>
          {React.cloneElement(this.props.component,{ customProps: this.props.object })}
      </div>
    );
  }
}

Working Code:

class Parent extends React.Component{
  render() {
    return(
      <Child a={1} comp={<GChild/>} />
    )
  }
}

class Child extends React.Component{
  constructor(){
    super();
    this.state = {b: 1};
    this.updateB = this.updateB.bind(this);
  }
  
  updateB(){
    this.setState(prevState => ({b: prevState.b+1}))
  }
  
  render(){
    var Comp = this.props.comp;
    return (
      <div>
        {React.cloneElement(Comp, {b: this.state.b})}
        <button onClick={this.updateB}>Click to update b</button>
      </div>
    );
  }
}

const GChild = props => <div>{JSON.stringify(props)}</div>;
 
ReactDOM.render(
  <Parent />,
  document.getElementById('container')
);
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>

<div id='container' />

You can do in the same as you did for SomeInnerComponent.

Just pass named props.

Inside CustomForm,

render() {

  const MyComponent = this.props.component; //stored it in some variable

    return (
      <div> 
         <MyComponent customProps = {this.props.object} /> //access object here and passed it or passed individual props
      </div>
    );
  }

EDIT :

Please find the working demo here.