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Inclusion Criteria:

* Participant must be at least 12 years of age at the time of signing the informed consent.
* Participants who have undergone allo-HCT.
* Participants with active moderate to severe cGVHD at the time of enrollment, defined using the NIH Consensus diagnosis and staging criteria for which the physician believes a new line of systemic therapy is required.
* Participant receiving systemic CNI and/or CS must be on a stable dose/regimen (prednisone equivalent \<1 mg/kg/day for CS) for at least 2 weeks prior to randomization.
* cGVHD is refractory to, or has recurred following, at least 2 prior lines of systemic treatment. Participants must have received a minimum of 2 and a maximum of 5 prior systemic therapies for cGVHD.
* Participant must have received ruxolitinib for the treatment of cGVHD unless the Investigator believes treatment with ruxolitinib for cGVHD was not suitable for the participant.
* Participants and/or their LAR must accept to be treated with 1 of the following BAT options as recommended to them by the Investigator on Cycle 1 Day 1:

  * ECP,
  * Low-dose MTX,
  * MMF,
  * Rituximab,
  * mTOR inhibitors (sirolimus, everolimus)
  * Imatinib,
  * Ibrutinib,
  * Proteasome inhibitors,
  * Pentostatin.
* Body weight ≥ 30 kg I 09. Life expectancy of \> 6 months.
* Contraceptive use by men and women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.

Exclusion Criteria:

* Any evidence (histologic, cytogenetic, molecular, hematologic, or mixed) of progressive or relapsed underlying disease or post-transplant lymphoproliferative disease after most recent allo-HCT.
* Participants who meet any of the following criteria regarding systemic cGVHD treatments:

  * Participants who newly initiated any systemic cGVHD treatment within 14 days prior to the date of randomization.
  * Participants receiving systemic ruxolitinib treatment who are unable to meet the following requirements:
* Ruxolitinib must be tapered and discontinued within 14 days following the first dose of belumosudil or BAT (allowing for a maximum overlap period of up to 14 days with belumosudil or BAT treatment).
* No dose increases of ruxolitinib are permitted from 14 days prior to the date of randomization until permanent discontinuation of ruxolitinib (dose reductions and discontinuations are permitted during this period).

  * Participants receiving other systemic cGVHD treatment (apart from CS and CNI) including investigational treatments who have not completed a washout period of at least 14 days or 5 half-lives (whichever is shorter) prior to the first dose of belumosudil or BAT treatment.

Note: Topical and organ-specific treatment for cGVHD and other supportive agents are allowed.

* Participant has had previous exposure to belumosudil.
* Participants with a Karnofsky Performance Scale (KPS) score \<60 (if aged ≥16 years) or Lansky Performance Score of \<60 (if aged \<16 years).
* Clinically uncontrolled chronic or ongoing infectious disease requiring antibiotic, antiviral, or antifungal treatment within 14 days prior to the date of randomization.
* Impairment of GI function (unrelated to cGVHD) or GI disease (unrelated to cGVHD) that may significantly alter the absorption of belumosudil (such as ulcerative disease, malabsorption syndrome, uncontrolled nausea, vomiting, diarrhea, or small bowel resection).
* Administration of live or live-attenuated vaccines is prohibited within 28 days or 5 elimination half-lives of the respective vaccine, whichever is longer, prior to study treatment administration and until study intervention discontinuation.
* Has a forced expiratory volume in the first second (FEV1) ≤39% or has lung score of 3 according to 2014 NIH consensus diagnostic and staging criteria.
* Has any of the following lab results:

  * Absolute neutrophil count \<1.0 × 109/L. The use of G-CSF is not allowed within 7 days before the screening hematological test.
  * Platelet count \<25 × 109/L. Platelet transfusions are not allowed within 72 hours before the screening hematological test.
  * ALT and/or AST \>3 × ULN (\>5 × ULN if abnormalities are due to cGVHD).
  * Total bilirubin \>1.5 × ULN (\>3 × ULN if Gilbert's syndrome or due to cGVHD).
  * eGFR \<30 mL/min/1.73 m2 using the MDRD-4 variable formula (if aged ≥18 years) or using the Bedside Schwartz formula (if aged \<18 years).
* Participants with active viral diseases
* Diagnosed or treated for another malignancy other than the underlying disease allo-HCT was indicated for, within 3 years prior to randomization with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in-situ malignancy, or low risk prostate cancer after curative therapy.

The above information is not intended to contain all considerations relevant to a participant's potential participation in a clinical trial.