I am currenty applying for disability. I was married for 9 years and 10 months, so I do not qualify to file for benefits under the 10 year mark. However, I do have evidence that we lived together for 4 years prior to the marriage, such as the taxes and my oldest son birth certificate. We never entered into a common law agreement since in PR that is not valid. Would it be possible to provide proof and be able to claim benefits under my ex husband?
You could apply, but assuming that your marriage ended in divorce rather than death it doesn't sound you'd be eligible. You must have been married for at least 10 full years in order to potentially qualify for divorced spousal benefits. A legally established common law marriage can count, but even in states that recognize common law marriage an intent to marry is required.
That said, the worst thing that would happen if you applied for divorced spousal benefits is that your claim would be disallowed. So, if you meet the other requirements for divorced spousal benefits you may still want to go ahead and give it a try. Note, however, that if your ex is still living, the earliest you could potentially qualify for divorced spousal benefits is age 62. There is no earlier eligibility for divorced spousal benefits on the basis of disability unless your ex is deceased (https://www.ssa.gov/OP_Home/handbook/handbook.03/handbook-0311.html).