Federated fine‑tuning with Low‑Rank Adaptation (LoRA) reduces communication and compute overhead by training and exchanging compact trainable factors. Clients may choose different LoRA ranks to respect their communication budgets and local adaptation needs. The server must reconcile these differences during aggregation and then construct rank‑specific adapters for each client. We separate this workflow into pre‑aggregation alignment (matching factor dimensions and scaling conventions) and rank‑specific LoRA adapter extraction (building client‑sized factor pairs from the aggregated global model). Two typical extraction strategies are direct rank truncation and dense Singular Value Decomposition (SVD). Direct truncation keeps the leading columns of one aggregated factor and the corresponding rows of the other; it is cheap but can increase reconstruction error. Dense SVD first forms the product of the aggregated LoRA factors, then decomposes this matrix and retains the top singular components, yielding the optimal rank‑constrained approximation in Frobenius norm at the cost of substantial computation. To balance accuracy and efficiency, we propose RBLA+, an extension of RBLA that employs compact QR/core‑SVD decomposition to minimize Frobenius error of the extracted LoRA update without forming the dense update, and it harmonizes client‑server scaling conventions during upload and broadcast. Across vision and language benchmarks, RBLA+ improves accuracy over RBLA in various heterogeneous settings, and CPU synthetic‑adapter tests show lower extraction time than the dense partial‑SVD baseline. RBLA+ preserves each client’s prescribed adapter size and per‑round communication payload, offering a practical trade‑off between performance and cost.\n\nReview: RBLA+ demonstrates that careful matrix factorization can dramatically cut the overhead of rank‑specific LoRA extraction while keeping communication budgets unchanged, making heterogeneous federated fine‑tuning more deployable.