Often, yes. The investor must show her capital was obtained lawfully, and for inherited funds that reaches the estate's origin where the amount is significant. The decedent's tax returns and asset records over a period of years usually suffice; a perfect lifetime account is not expected.
Lawful source extends one generation back when the sum is large
EB-5 capital must be obtained through lawful means, and the investor must demonstrate that by a preponderance of the evidence. For an inheritance, the first layer is the transfer itself: the will, the probate or notarial documents, the estate accounting and the bank record of the distribution establish that she received the money as a beneficiary. USCIS may look one layer further, particularly where the inheritance supplies most of the investment, and ask how the decedent came to hold the assets.
The answer does not require reconstructing a career; it requires a coherent explanation supported by documents such as the decedent's income tax returns for a reasonable period, the sale records of a property or business that produced the estate's cash, pension or investment statements and, where records are missing because of age, a sworn statement from the executor or a family member describing what is known. The standard is credibility and consistency rather than completeness. A file that acknowledges what cannot be found and explains why is treated far better than one that omits the question.