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The B1 is appropriate for you to use for the 4 weeks of meetings as long as you are being paid by the UK company. Your employment letter will need to detail the nature of the meetings you will be part of for those 4 weeks and that you will be paid by the UK company for your attendance at those meetings.
To work off shore for more than 29 days you may use the B1 stamp in your passport and do not have to have the visa annotated OCS.
.OCS workers already in possession of a valid B1/B2 visa do not need to apply for a new visa and may travel with a copy of the Coast Guard letter to explain the purpose of a trip at port of entry. If they prefer having an annotated B1 (OCS) to avoid more rigorous immigration inspection, they may apply for that specific visa, but their B1/B2 visa will be cancelled.
Since you will be doing a combo with on shore meetings requiring the B1 and off shore (I assume for more than 29 days) you will need the Coast Guard letter.
In addition to the Coast Guard letter you will need an employer letter naming the vessel or platform the employee will be working on, the length of time the employee will be performing services, and a U.S. Coast Guard Exemption Letter confirming that the vessel or platform named in the employer letter from OCSLA regulations requiring citizenship or permanent residency for employees.
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