Can a man be infected with Clamydia and pass it to a woman even if a condomen is used? Or can it be transferred through oral sex to a woman?

If a condom is used, unlikely. However, condoms are not foolproof.
Yes, Chlamydia can be transmitted during oral sex. A good fact sheet on Chlamydia can be found on the Center For Disease Control's website:
STD Facts - Chlamydia

Yes, it can be transmistted, a condom does help but my not always be 100 percent

condom = 98.5%, no sex= 100% protection.

Yes, it can be transmitted by intimate sexual contact. But a condom should give you lots of protection. There's more info about it here: Chlamidya Tests from chlamydia-tests.co.uk

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Chlamydia Tests and Information about Chlamydia