diff --git a/src/lightning/fabric/CHANGELOG.md b/src/lightning/fabric/CHANGELOG.md
index 27ec226acc0b0..64ea5fc408344 100644
--- a/src/lightning/fabric/CHANGELOG.md
+++ b/src/lightning/fabric/CHANGELOG.md
@@ -135,6 +135,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Fixed an issue with hpu imports leading to performance degradation  ([#17788](https://github.com/Lightning-AI/lightning/pull/17788))
 
 
+- Fixed check for FSDP's flat parameters in all parameter groups ([#17914](https://github.com/Lightning-AI/lightning/pull/17914))
+
+
 ## [2.0.3] - 2023-06-07
 
 - Added support for `Callback` registration through entry points ([#17756](https://github.com/Lightning-AI/lightning/pull/17756))
diff --git a/src/lightning/fabric/strategies/fsdp.py b/src/lightning/fabric/strategies/fsdp.py
index c09e91fa87f2a..09c24a444fcdf 100644
--- a/src/lightning/fabric/strategies/fsdp.py
+++ b/src/lightning/fabric/strategies/fsdp.py
@@ -637,11 +637,13 @@ def _init_cpu_offload(cpu_offload: Optional[Union[bool, "CPUOffload"]]) -> "CPUO
 def _optimizer_has_flat_params(optimizer: Optimizer) -> bool:
     _FSDP_FLATTENED = "_fsdp_flattened"
     if _TORCH_GREATER_EQUAL_1_13:
-        return any(getattr(param, _FSDP_FLATTENED, False) for param in optimizer.param_groups[0]["params"])
+        return any(
+            getattr(param, _FSDP_FLATTENED, False) for group in optimizer.param_group for param in group["params"]
+        )
 
     from torch.distributed.fsdp import FlatParameter
 
-    return any(isinstance(param, FlatParameter) for param in optimizer.param_groups[0]["params"])
+    return any(isinstance(param, FlatParameter) for group in optimizer.param_groups for param in group["params"])
 
 
 def _get_sharded_state_dict_context(module: "FullyShardedDataParallel") -> _GeneratorContextManager:
diff --git a/tests/README.md b/tests/README.md
index 637c7ccbc0834..b042044e12e09 100644
--- a/tests/README.md
+++ b/tests/README.md
@@ -12,7 +12,7 @@ To setup a local development environment, install both local and test dependenci
 git clone https://github.com/Lightning-AI/lightning.git
 cd lightning
 
-# install required depedencies
+# install required dependencies
 export PACKAGE_NAME=pytorch
 python -m pip install ".[dev, examples]"
 # install pre-commit (optional)