For simple solution, remove the custom modulemap, let CocoaPods generate one instead

SDWebImage.podspec

@@ -23,7 +23,6 @@ Pod::Spec.new do |s|
 
   s.requires_arc = true
   s.framework = 'ImageIO'
-  s.module_map = 'WebImage/SDWebImage.modulemap'
   
   s.default_subspec = 'Core'
 

SDWebImage.xcodeproj/project.pbxproj

@@ -391,7 +391,6 @@
 		32F7C07D2030719600873181 /* UIImage+Transform.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = "UIImage+Transform.h"; sourceTree = "<group>"; };
 		32FDE87A2088871B008D7530 /* MKAnnotationView+WebCache.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; path = "MKAnnotationView+WebCache.m"; sourceTree = "<group>"; };
 		32FDE87B2088871B008D7530 /* MKAnnotationView+WebCache.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = "MKAnnotationView+WebCache.h"; sourceTree = "<group>"; };
-		32FDE8A4208887A6008D7530 /* SDWebImage.modulemap */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = "sourcecode.module-map"; path = SDWebImage.modulemap; sourceTree = "<group>"; };
 		4369C2751D9807EC007E863A /* UIView+WebCache.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; name = "UIView+WebCache.h"; path = "SDWebImage/UIView+WebCache.h"; sourceTree = "<group>"; };
 		4369C2761D9807EC007E863A /* UIView+WebCache.m */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.objc; name = "UIView+WebCache.m"; path = "SDWebImage/UIView+WebCache.m"; sourceTree = "<group>"; };
 		4397D2F41D0DE2DF00BB2784 /* NSImage+Compatibility.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; path = "NSImage+Compatibility.h"; sourceTree = "<group>"; };
@@ -605,7 +604,6 @@
 			isa = PBXGroup;
 			children = (
 				4A2CAE021AB4BB5400B6BC39 /* Info.plist */,
-				32FDE8A4208887A6008D7530 /* SDWebImage.modulemap */,
 			);
 			name = "Supporting Files";
 			sourceTree = "<group>";

WebImage/SDWebImage.modulemap

@@ -1,19 +0,0 @@
-framework module SDWebImage {
-  umbrella header "SDWebImage.h"
-  
-  // until CocoaPods fix the bug when using modular headers in #8879
-  // we have to exclude Private Headers manually even we use Podspec `private_header_files` syntax
-  exclude header "SDWeakProxy.h"
-  exclude header "SDInternalMacros.h"
-  exclude header "SDmetamacros.h"
-  exclude header "NSBezierPath+RoundedCorners.h"
-  exclude header "UIColor+HexString.h"
-  exclude header "SDAsyncBlockOperation.h"
-  exclude header "SDImageAPNGCoderInternal.h"
-  exclude header "SDImageGIFCoderInternal.h"
-  exclude header "SDImageCachesManagerOperation.h"
-  exclude header "SDImageAssetManager.h"
-
-  export *
-  module * { export * }
-}