The treatment regimen will consist of 4 doses of FPI-2265

The treatment regimen will consist of 4 doses of FPI-2265, administered at 8 ± 1 week intervals, with an initial activity of 100 kilobecquerel (kBq)/kg (±10%).

Additional doses will be administered at 100 kBq/kg (±10%) with the following exceptions:

• Participants who experience dose-modifying events.
• Participants with a confirmed decline in PSA>=50%.

Inclusion Criteria:

1. Participants aged ≥ 18 years.

2. Participants must have the ability to understand and sign an approved informed consent (ICF).

3. Participants must have the ability to understand and comply with all protocol requirements.

4. Adenocarcinoma of prostate proven by histopathology.

5. Life expectancy of 6 months or more.

6. Unresectable metastases.

7. Documented progressive disease (PD); progressive mCRPC will be based on at least 1 of the following criteria:

   1. Serum PSA progression is defined as 2 consecutive increases in PSA over a previous reference value measured at least 1 week prior. The minimal starting value is 1.0 ng/mL, if PSA is the only indication of progression.
   2. Soft-tissue progression defined as an increase ≥ 20% in the sum of the diameter (SOD) (short axis for nodal lesions and long axis for non-nodal lesions) of all target lesions based on the smallest SOD since treatment started or the appearance of one or more new lesions.
   3. Progression of bone disease: evaluable disease or new bone lesions(s) by bone scan (2+2 PCWG3 criteria).

8. If known Breast Cancer gene (BRCA) mutations are present, participants should have received FDA approved therapies such as poly-ADP ribose polymerase (PARP) inhibitors and progressed.

9. Castration resistant disease with confirmed testosterone level ≤ 50 ng/dL under prior androgen deprivation therapy (ADT). Must have a castrate level of serum testosterone (< 50 ng/dL or < 1.7 nmol/L).

10. Positive PSMA PET/CT scans, obtained with approved PSMA-ligands, defined as at least one PSMA-positive metastatic lesion and no PSMA-negative lesions.

11. ECOG-PS 0 to 1.

12. Hemoglobin (Hgb) concentration ≥ 9.0 g/dL.

13. Platelet counts ≥ 100 × 10^9/L.

14. White blood cell (WBC) count ≥ 2.0 × 10^9/L, absolute neutrophil count (ANC) > 1.5 × 10^9/L.

    a. Hematological criteria cannot be met with ongoing or recent blood transfusions (within 7 days prior to the scheduled first dose of study treatment) or require growth factor support (within 21 days prior to the scheduled first dose of study treatment).

15. Alanine aminotransferase or aspartate aminotransferase ≤ 3.0 × upper limit of normal (ULN).

16. Serum total bilirubin ≤ 1.5 × ULN; in participants with Gilbert's syndrome, a total bilirubin ≤ 3 times ULN and direct bilirubin within normal limits are permitted.

17. Albumin ≥ 2.5 g/dL.

18. Serum/plasma creatinine ≤ 1.5 × ULN or creatinine clearance ≥ 60 mL/min based on the Cockcroft-Gault formula.

19. Prothrombin time, international normalized ratio or prothrombin time test < 1.5 × ULN.

20. Received ≥ 1 androgen receptor axis-targeted therapies (ARAT).

21. Participants on anti-androgen therapy are allowed to continue their treatment at the discretion of their treating physician.

Exclusion Criteria:

1. Less than 6 weeks from enrollment since last myelosuppressive therapy (including Docetaxel, Cabazitaxel, 223Ra, 153Sm, 177Lu-PSMA-617/other Lu-PSMA RLT or any other radionuclide therapy). Participants who received previous treatment with Ac-225 are excluded.

2. Participants who received more than 4 prior lines of systemic therapy for CRPC.

3. Urinary tract obstruction as evidenced by Tc-99m DTPA renal scan with diuretics.

4. Participants with skeletal metastases presenting as a superscan on a 99m Tc MDP Bone Scan.

   Superscan is defined as a bone scan which demonstrates markedly increased skeletal radioisotope uptake relative to soft tissues in association with absent or faint renal activity (absent kidney sign).

5. Persistent baseline dry eye or dry mouth > Grade 1 from prior RLT.

6. Persistent prior AEs > Grade 1 from prior anti-cancer therapies.

7. Abnormal renal function (estimated glomerular filtration rate < 60 mL/min), baseline Hgb < 9g/dL, ANC < 1.5 ×10^9/L, platelets < 100 ×10^9/L, and prothrombin time, international normalized ratio or prothrombin time test ≥ 1.5 × ULN.

8. Administration of an investigational agent ≤ 60 days or 5 half-lives, whichever is shorter, prior to Cycle 1, Week 0.

9. Known presence of central nervous system (CNS) metastases or liver metastases.

10. Active malignancy other than low-grade non-muscle-invasive bladder cancer and non-melanoma skin cancer.

11. Concurrent illness that may jeopardize the participant's ability to undergo study procedures as determined by the Investigator.

12. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression.

13. Concurrent serious (as determined by the investigator) medical conditions, including, but not limited to, New York Heart Association Class III or IV congestive heart failure, unstable ischemia, uncontrolled symptomatic arrhythmia, history of congenital prolonged QT syndrome, uncontrolled infection, known active hepatitis B or C, or other significant co-morbid conditions that in the opinion of the Investigator would impair study participation or cooperation.

14. Major surgery ≤ 30 days prior to enrollment.

15. Planning to conceive pregnancy during the treatment and up to 6 months after the last treatment.