The declaration declare module 'shiitake'; should be in a global scope. i.e. a top-level declaration in a non-module (where a module is a file with at least one top-level import or export).
A declaration of the form declare module '...' { } in a module is an augmentation. For more details see Typescript Module Augmentation.
So you want this file to look like this:
declare module 'shiitake' {
import * as React from 'react';
export interface ShiitakeProps {
lines: number;
}
export default class Shiitake extends React.Component<ShiitakeProps, any> {
}
}