diff --git a/parso/python/tokenize.py b/parso/python/tokenize.py
index 20b80be..11b9a85 100644
--- a/parso/python/tokenize.py
+++ b/parso/python/tokenize.py
@@ -419,8 +419,6 @@ def tokenize_lines(lines, version_info, start_pos=(1, 0)):
                 tos = fstring_stack[-1]
                 if not tos.is_in_expr():
                     string, pos = _find_fstring_string(endpats, fstring_stack, line, lnum, pos)
-                    if pos == max:
-                        break
                     if string:
                         yield PythonToken(
                             FSTRING_STRING, string,
@@ -431,6 +429,8 @@ def tokenize_lines(lines, version_info, start_pos=(1, 0)):
                         )
                         tos.previous_lines = ''
                         continue
+                    if pos == max:
+                        break
 
                 rest = line[pos:]
                 fstring_end_token, additional_prefix, quote_length = _close_fstring_if_necessary(
diff --git a/test/test_fstring.py b/test/test_fstring.py
index 4c85de8..a0d346d 100644
--- a/test/test_fstring.py
+++ b/test/test_fstring.py
@@ -79,11 +79,17 @@ def test_tokenize_start_pos(code, positions):
     assert positions == [p.start_pos for p in tokens]
 
 
-def test_roundtrip(grammar):
-    code = dedent("""\
-        f'''s{
-           str.uppe
-        '''
-        """)
+@pytest.mark.parametrize(
+    'code', [
+        dedent("""\
+            f'''s{
+               str.uppe
+            '''
+            """),
+        'f"foo',
+        'f"""foo',
+    ]
+)
+def test_roundtrip(grammar, code):
     tree = grammar.parse(code)
     assert tree.get_code() == code