diff --git a/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/FunctionPostProcessingTests.java b/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/FunctionPostProcessingTests.java
index 24bcc3d0b..621251304 100644
--- a/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/FunctionPostProcessingTests.java
+++ b/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/FunctionPostProcessingTests.java
@@ -17,6 +17,7 @@
 package org.springframework.cloud.stream.function;
 
 import java.util.function.Function;
+import java.util.function.Supplier;
 
 import org.junit.jupiter.api.Test;
 
@@ -29,8 +30,10 @@
 import org.springframework.cloud.stream.binder.test.TestChannelBinderConfiguration;
 import org.springframework.context.ConfigurableApplicationContext;
 import org.springframework.context.annotation.Bean;
+import org.springframework.context.annotation.Configuration;
 import org.springframework.integration.support.MessageBuilder;
 import org.springframework.messaging.Message;
+import org.springframework.messaging.support.GenericMessage;
 
 import static org.assertj.core.api.Assertions.assertThat;
 
@@ -76,6 +79,22 @@ void successfulPostProcessingOfSingleFunction() {
 		}
 	}
 
+	@Test
+	void successfulPostProcessingOfSupplierFunctionCompposition() throws Exception {
+		System.clearProperty("spring.cloud.function.definition");
+		try (ConfigurableApplicationContext context = new SpringApplicationBuilder(
+			TestChannelBinderConfiguration.getCompleteConfiguration(SupplierPostProcessingTestConfiguration.class))
+			.web(WebApplicationType.NONE).run("--spring.jmx.enabled=false",
+					"--spring.cloud.function.definition=hello|uppercase",
+					"--spring.cloud.stream.bindings.hellouppercase-out-0.producer.poller.fixed-delay=100")) {
+			Thread.sleep(1000);
+			OutputDestination outputDestination = context.getBean(OutputDestination.class);
+
+			assertThat(outputDestination.receive(5000, "hellouppercase-out-0").getPayload()).isEqualTo("HELLO".getBytes());
+			assertThat(context.getBean(SupplierPostProcessingTestConfiguration.class).postProcessed).isTrue();
+		}
+	}
+
 	@Test
 	void noPostProcessingOnError() {
 		System.clearProperty("spring.cloud.function.definition");
@@ -207,6 +226,31 @@ public Function<String, String> reverse() {
 		}
 	}
 
+	@EnableAutoConfiguration
+	@Configuration
+	public static class SupplierPostProcessingTestConfiguration {
+
+		public static boolean postProcessed;
+
+		@Bean
+		public Supplier<Message<String>> hello() {
+			return () -> new GenericMessage<>("hello");
+		}
+
+		@Bean
+		public Function<String, String> uppercase() {
+			return new PostProcessingFunction<String, String>() {
+				public String apply(String input) {
+					return input.toUpperCase();
+				}
+
+				public void postProcess(Message<String> result) {
+					postProcessed = true;
+				}
+			};
+		}
+	}
+
 	private static class SingleFunctionPostProcessingFunction implements PostProcessingFunction<String, String> {
 
 		private boolean success;
diff --git a/core/spring-cloud-stream/src/main/java/org/springframework/cloud/stream/function/FunctionConfiguration.java b/core/spring-cloud-stream/src/main/java/org/springframework/cloud/stream/function/FunctionConfiguration.java
index c051e777b..b6d80bc2f 100644
--- a/core/spring-cloud-stream/src/main/java/org/springframework/cloud/stream/function/FunctionConfiguration.java
+++ b/core/spring-cloud-stream/src/main/java/org/springframework/cloud/stream/function/FunctionConfiguration.java
@@ -107,6 +107,7 @@
 import org.springframework.messaging.MessageHeaders;
 import org.springframework.messaging.MessagingException;
 import org.springframework.messaging.SubscribableChannel;
+import org.springframework.messaging.support.ChannelInterceptor;
 import org.springframework.scheduling.TaskScheduler;
 import org.springframework.scheduling.Trigger;
 import org.springframework.scheduling.support.CronTrigger;
@@ -235,15 +236,22 @@ InitializingBean supplierInitializer(FunctionCatalog functionCatalog, StreamFunc
 						}
 
 						if (functionWrapper != null) {
+							FunctionInvocationWrapper postProcessor = functionWrapper;
 							IntegrationFlow integrationFlow = integrationFlowFromProvidedSupplier(new PartitionAwareFunctionWrapper(functionWrapper, context, producerProperties),
 									pollable, context, taskScheduler, producerProperties, outputName)
+									.intercept(new ChannelInterceptor() {
+										public void postSend(Message<?> message, MessageChannel channel, boolean sent) {
+											postProcessor.postProcess();
+										}
+									})
 									.route(Message.class, message -> {
 										if (message.getHeaders().get("spring.cloud.stream.sendto.destination") != null) {
 											String destinationName = (String) message.getHeaders().get("spring.cloud.stream.sendto.destination");
 											return streamBridge.resolveDestination(destinationName, producerProperties, null);
 										}
 										return outputName;
-									}).get();
+									})
+									.get();
 							IntegrationFlow postProcessedFlow = (IntegrationFlow) context.getAutowireCapableBeanFactory()
 									.initializeBean(integrationFlow, integrationFlowName);
 							context.registerBean(integrationFlowName, IntegrationFlow.class, () -> postProcessedFlow);