Yes, if this is how you are choosing to file your Missouri part-year return. Your part-year return in MO can be done one of two ways: you may file all of your income as if it were taxable in Missouri as a resident, and then take a percentage for the amount of the tax based on the amount of income you actually earned there, or you may claim a credit for the taxes you paid to the state and political subdivisions for the income you earned there once you moved. Since you are using method 2, the credit, you may claim the taxes paid to PA (which is the amount withheld minus the refund) as well as the amount paid to Philadelphia (amount withheld minus the refund, if any).
Here is a website that describes this treatment, as well as links to assist you: http://dor.mo.gov/faq/personal/nonresident.php
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