diff --git a/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/HeaderTests.java b/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/HeaderTests.java
index 45302209f0..1b6366b5aa 100644
--- a/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/HeaderTests.java
+++ b/core/spring-cloud-stream-integration-tests/src/test/java/org/springframework/cloud/stream/function/HeaderTests.java
@@ -129,6 +129,24 @@ void checkMessageWrappedFunctionalConsumer() {
 		assertThat(headers.get(MessageHeaders.CONTENT_TYPE)).isEqualTo("application/json");
 	}
 
+	@Test
+	void timestampHeaderIsPresentOnConsumedMessage() {
+		try (ConfigurableApplicationContext context = new SpringApplicationBuilder(
+			TestChannelBinderConfiguration.getCompleteConfiguration(FunctionUpperCaseConfiguration.class))
+			.web(WebApplicationType.NONE)
+			.run("--spring.jmx.enabled=false",
+				"--spring.cloud.function.definition=uppercase")) {
+
+			InputDestination input = context.getBean(InputDestination.class);
+			input.send(new GenericMessage<>("hello".getBytes()), "uppercase-in-0");
+
+			OutputDestination output = context.getBean(OutputDestination.class);
+			Message<byte[]> result = output.receive(1000, "uppercase-out-0");
+
+			assertThat(result.getHeaders().getTimestamp()).isNotNull();
+		}
+	}
+
 	@EnableAutoConfiguration
 	public static class EmptyConfiguration {
 
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 2c0e9bec0f..5ff18d010b 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
@@ -113,6 +113,7 @@
 import org.springframework.messaging.MessagingException;
 import org.springframework.messaging.SubscribableChannel;
 import org.springframework.messaging.support.ChannelInterceptor;
+import org.springframework.messaging.support.GenericMessage;
 import org.springframework.scheduling.TaskScheduler;
 import org.springframework.scheduling.Trigger;
 import org.springframework.scheduling.support.CronTrigger;
@@ -409,12 +410,19 @@ private <T> Message<T> wrapToMessageIfNecessary(T value) {
 	}
 
 	private static <P> Message<P> sanitize(Message<P> inputMessage) {
-		return MessageBuilder
+		Message<P> sanitized = MessageBuilder
 			.fromMessage(inputMessage)
 			.removeHeader("spring.cloud.stream.sendto.destination")
-//			.setHeader(MessageUtils.SOURCE_TYPE, inputMessage.getHeaders().get(MessageUtils.TARGET_PROTOCOL))
-//			.removeHeader(MessageUtils.TARGET_PROTOCOL)
 			.build();
+		if (sanitized == inputMessage) {
+			// MessageBuilder.build() returns the same instance when no header was
+			// actually modified (fast-path in BaseMessageBuilder), which skips the
+			// GenericMessage constructor and therefore skips stamping a "timestamp"
+			// header. Force a fresh GenericMessage so the header is always present,
+			// restoring pre-4.3.3 behavior. See GH-3211.
+			sanitized = new GenericMessage<>(inputMessage.getPayload(), inputMessage.getHeaders());
+		}
+		return sanitized;
 	}
 
 	private static class FunctionToDestinationBinder implements InitializingBean, ApplicationContextAware {