ObjectiveC target can't find module, Swift working fine - objective-c

Question

I'm building a framework that needs to work with Swift and Objective-C. It is built with Swift.
It works fine in a Swift app. #import MyFrameworkName works just as expected. But I can't seem to make it work in an Objective-C app.
#import <MyFrameworkName/MyFrameworkName-Swift.h>
This is the build log:
<module-includes>:1:9: note: in file included from <module-includes>:1:
#import "Headers/MyFrameworkName.h"
^
/Users/user/Projects/MyFrameworkName/Sources/MyFrameworkName.h:20:9: error: module 'CommonCryptoBridge' not found
#import CommonCryptoBridge;
^
<unknown>:0: error: could not build Objective-C module 'MyFrameworkName'
This is my framework header:
#import <UIKit/UIKit.h>
FOUNDATION_EXPORT double MyFrameworkNameVersionNumber;
FOUNDATION_EXPORT const unsigned char MyFrameworkNameVersionString[];
#import CommonCryptoBridge;
The CommonCryptoBridge is a module to enable CommonCrypto in Swift, defined by CommonCryptoBridge.h and CommonCryptoBridge.modulemap:
CommonCryptoBridge.h
#ifndef __COMMONCRYPTO_BRIDGE__
#include <CommonCrypto/CommonCrypto.h>
#define __COMMONCRYPTO_BRIDGE__
#endif /* __COMMONCRYPTO_BRIDGE__ */
CommonCryptoBridge.modulemap
module CommonCryptoBridge [system] {
header "CommonCryptoBridge.h"
export *
}