You'll want to process a custody change first, which will place the record in the custody of the partner, so you can then process the transfer in. 

In order to begin the custody change, go to the person record > animals tab, and select the green action button on the animal record you need to intake. Select the 'Transfer Custody to Partner' option.

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After filling out the custody change form, go to the Partner Record > Custody Changes tab. From there you will be able to process the transfer in.