I think the answer is likely YES, however, your question is somewhat vague.
I understand you to say you created graphics for company A, and still have the graphics. Company B bought Company A, including its IP, and now you would like to use those graphics for Company B. If that is correct, then the answer seems to be YES. That is because either you still own the copyright to the graphics subject to an express or implied license from your studio to Company A to use them for the intended purpose or Company A owned them. Since Company A appears to have sold any such license or ownership to Company B, its seems that in either situation you would have the right to use them for Company B if Company B authorizes you to do so.
However, that is just an educated guess based on your vague statement of facts and the applicable law. You really should see an IP attorney to be sure your specific facts do not change this general answer.
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Based only on the facts you provide, yes, it sounds like the new owner purchased the right to continue to use the trademarks that the old owner used to brand the business. Even though the word "trademark" is not in the sentence you quote, a trademark is a type of intellectual property and, if a logo, is copyrightable as well -- so the business' trademarks fit into two categories that are listed in the sentence you quote. It makes much sense to reach out, however, to the former owner and have him send you an email confirming that all the materials you have on hand can be used for the new owner's benefit. Of course, you should discuss this all with your own trademark attorney who will evaluate the contract that you quote. Very often one provision of a contract [like the section you quote] can only be properly interpreted in light of other provisions.
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I guess I'm confused about who did what here and who you are.
Your query refers to someone who is or was a "customer," presumably of your business, and somehow the business bought some artwork and a license to use the customer's IP. And your query asks about what a "new owner" can use, which I guess is you since your query states you own this studio, even though you're using the 3rd person as if you're not the new owner.
So I gather you just bought this studio and you found this file of this sale. Since your headline asks about artwork, yes, artwork is IP, but your business may have bought some actual copyrightable art, rather than the copyrights to that art. Your business also bought this license, so there's your right to use the copyrights and make reproductions, derivative works, etc. But unless your contract says your business OWNS the copyrights, then it's only got a license, and can't sell the copyrights.
For safety's sake, night be best to see a business/IP lawyer to get your contract reviewed.
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The first question is who owns what intellectual property rights in the artwork from the get-go. If you had a written contract, then you may have either assigned the copyright and other intellectual property rights to the client, or the client could own such rights as a work-made-for-hire.
If there was no written agreement governing your creation of the work, then you would own the copyright in the work, and the client would probably have an implied license to use the work. Also, the client would probably own common law trademark rights in the logo through its use of the logo in connection with goods/services.
Based on the language you have provided, it sounds like whatever copyright, trademark, or other IP rights (whether ownership or license/use rights) the client had were transferred to the new owner, so if the new owner is ok with you using the old logo, there would be no IP problem.
I suppose if you had some other terms in your original agreement with the client preventing use of the work for others, that could potentially pose a problem, but it's hard to know without full contract language.
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