Your employer is incorrect.
North Carolina says "A nonresident employee is subject to N. C. withholding tax on any part of his wages paid for services performed in this State."
See Employee Requirements in Withholding Tax Frequently Asked Questions.
You should report on a Pennsylvania income tax return the amount you earned until you moved to North Carolina.
You should not have been double taxed so do not claim a credit for tax paid to NC.
Instead adjust the income on the part-year NC return to show what you actually earned in NC. Since you are reporting less income than the amount income shown on your W-2, the extra withholding will be added back into your NC refund.
You don't have to send your pay stubs with your NC return. Keep them in case you are audited.
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