diff --git a/compiler/src/dotty/tools/dotc/interactive/Completion.scala b/compiler/src/dotty/tools/dotc/interactive/Completion.scala
index b57c300defae..1f26b50b6cce 100644
--- a/compiler/src/dotty/tools/dotc/interactive/Completion.scala
+++ b/compiler/src/dotty/tools/dotc/interactive/Completion.scala
@@ -24,6 +24,7 @@ import dotty.tools.dotc.printing.Texts._
 import dotty.tools.dotc.util.{NameTransformer, NoSourcePosition, SourcePosition}
 
 import scala.collection.mutable
+import scala.util.control.NonFatal
 
 /**
  * One of the results of a completion query.
@@ -61,6 +62,8 @@ object Completion {
    */
   def completionMode(path: List[Tree], pos: SourcePosition): Mode =
     path match {
+      case Ident(_) :: Import(_, _) :: _ =>
+        Mode.Import
       case (ref: RefTree) :: _ =>
         if (ref.name.isTermName) Mode.Term
         else if (ref.name.isTypeName) Mode.Type
@@ -211,6 +214,22 @@ object Completion {
         // import a.C
         def isSameSymbolImportedDouble =  denotss.forall(_.denots == first.denots)
 
+        def isScalaPackage(scopedDenots: ScopedDenotations) =
+          scopedDenots.denots.exists(_.info.typeSymbol.owner == defn.ScalaPackageClass)
+
+        def isJavaLangPackage(scopedDenots: ScopedDenotations) =
+          scopedDenots.denots.exists(_.info.typeSymbol.owner == defn.JavaLangPackageClass)
+
+        // For example
+        // import java.lang.annotation
+        //    is shadowed by
+        // import scala.annotation
+        def isJavaLangAndScala =
+          try
+            denotss.forall(denots => isScalaPackage(denots) || isJavaLangPackage(denots))
+          catch
+            case NonFatal(_) => false
+
         denotss.find(!_.ctx.isImportContext) match {
           // most deeply nested member or local definition if not shadowed by an import
           case Some(local) if local.ctx.scope == first.ctx.scope =>
@@ -218,6 +237,12 @@ object Completion {
 
           case None if isSingleImport || isImportedInDifferentScope || isSameSymbolImportedDouble =>
             resultMappings += name -> first.denots
+          case None if isJavaLangAndScala =>
+            denotss.foreach{
+              denots =>
+                if isScalaPackage(denots) then
+                  resultMappings += name -> denots.denots
+            }
 
           case _ =>
         }
diff --git a/language-server/test/dotty/tools/languageserver/CompletionTest.scala b/language-server/test/dotty/tools/languageserver/CompletionTest.scala
index bc870e329f4f..afee53328857 100644
--- a/language-server/test/dotty/tools/languageserver/CompletionTest.scala
+++ b/language-server/test/dotty/tools/languageserver/CompletionTest.scala
@@ -976,4 +976,22 @@ class CompletionTest {
               ("main", Module, "main")
             )
           )
+
+  @Test def i13623_annotation : Unit =
+    code"""import annot${m1}"""
+          .withSource
+          .completion(m1,
+            Set(
+              ("annotation", Module, "scala.annotation")
+            )
+          )
+
+  @Test def importAnnotationAfterImport : Unit =
+    code"""import java.lang.annotation; import annot${m1}"""
+        .withSource
+        .completion(m1,
+          Set(
+            ("annotation", Module, "scala.annotation")
+          )
+        )
 }