There are actually two separate issues.
The first issue is the method of accounting. Pursuant to
26 USC § 446, taxes are to be computed "under the method of accounting on the basis of which the taxpayer regularly computes his income in keeping his books". For almost all individuals, this is "the cash receipts and disbursements method" (commonly referred to as "cash basis" accounting). However, individuals are not actually required to use that accounting method. But let's assume you use that accounting method because almost everyone does.
Under the cash method, what matters is when you
received the income, not when you
earned it.
However, the discussion does not end there. The second issue is when you received the income.
Under any method of accounting, receipt of cash is not necessarily when the cash is physically available for you to spend. It could be earlier than that. Pursuant to
26 CFR 1.451-2, "Income although not actually reduced to a taxpayer's possession is constructively received by him in the taxable year during which it is credited to his account,
set apart for him, or otherwise made available so that he may draw upon it at any time, or so that
he could have drawn upon it during the taxable year if notice of intention to withdraw had been given. However, income is not constructively received if the taxpayer's control of its receipt is subject to substantial limitations or restrictions." (emphasis added)
In the situation in this thread, it sounds like the company was legally required to pay your wife in 2014 under her employment agreement with them. Accordingly, they set aside the funds to pay your wife in 2014 but failed to actually make the payment due to a clerical error. But if she had insisted on being paid in 2014 for it, they would have been legally obligated to comply. As a courtesy, she is allowing them to wait until 2015, but if she wanted, it sounds like she could have insisted on receiving the money in 2014 because it was due in 2014. If that understanding of the facts is correct, then under the regulation quoted, the income was received in 2014, so it is taxable in 2014, not 2015.
The regulation isn't exactly a model of clarity so you could probably make an argument for whichever year favours you more. It doesn't provide an election though.
