Keeping 2 private repos in sync across 2 different orgs

[wuebkers]

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We maintain a private repository within our organization where we utilize GitHub Projects extensively. Our objective is to synchronize this repository with a private repository hosted within a client's organization. However, establishing the two repositories on separate remotes would require granting access to the client's organization for every member of our team involved in the project and we are trying to avoid that. Is there a better way to keep these two repos in sync without our teams clogging up seats on the client's org?