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The EIN  99-9999000 has worked for several so far.  Form 2555 Instructions  state: 

Foreign earned income also doesn't include the following types of income. 

• Pension and annuity income (including social security benefits and railroad retirement benefits treated as social security).

Instead, you can subtract the nontaxable treaty income, see  United States Income Tax Treaties as Other Income.

Subtract the income

1. Miscellaneous Income, 1099-A, 1099-C, Start
2. Scroll to the bottom
3. Other reportable income, Start
4. Other taxable income?
5. Select YES
6. Description treaty exempt
7. Amount, enter as a negative using negative sign
8. continue

If the payee claims treaty benefits that override or modify any provision of the Internal Revenue Code, and by claiming these benefits the payee’s tax is, or might be, reduced, the payee must attach a fully completed Form 8833, Treaty-Based Return Position Disclosure Under Section 6114 or 7701(b), to the payee’s tax return.

Claiming Tax Treaty Benefits states:

The payee does not have to file Form 8833 for any of the following situations:

1. The payee can claim a reduced rate of withholding tax under a treaty on interest, dividends, rent, royalties, or other fixed or determinable annual or periodic income ordinarily subject to the 30% rate.
2. The payee can claim a treaty exemption that reduces or modifies the taxation of income from dependent personal services, pensions, annuities, social security and other public pensions, or income of artists, athletes, students, trainees, or teachers. This includes taxable scholarship and fellowship grants.
3. The payee can claim a reduction or modification of taxation of income under an International Social Security Agreement or a Diplomatic or Consular Agreement.
4. The payee is a partner in a partnership, or a beneficiary of an estate or trust and the partnership, estate, or trust reports the required information on its return.
5. The payments or items of income that are otherwise required to be disclosed total no more than $10,000.

@juham2013