You can merge collections in LUNA v7.1.5+ using the data export feature. The LUNA Library allows you to add media items from one collection to another collection and export your data as a .csv file from one of your collections so that you can import the data into another collection. It will require a little work on your part to make sure the data you are re-importing adheres to the data schema of the collection you're importing the data to. If the schemas are the same or similar, this will make it easier to do.
Once all media items have been added, the last step is to upload the data you exported from the first collection. To link the images to the data, select the appropriate linking field and the option for "Any media items and records in collection (slow)".
When deleting media items that have been moved to a different collection DO NOT DELETE the items from their batches or the batch itself in the Uploader. Use the Library only to delete the media items, otherwise they will be deleted completely from the system, including the collection they were just added to.
Depending on how many images are in the collection you're moving, you may choose to work in batches. See Tips and tricks to set a page size in the LUNA Library.
If the collection you are moving does not already have a field that includes the media item filename for linking records to media, you can select the internal field Media Filename as an Export option: