InlineUIContainers are not copyable elements. Thus, when you copy a part of the document that includes an inline UI container and some text and paste it, only the text will be placed. You can find a more detailed explanation in this forum thread.
When it comes to inserting text in the document, this can be done through the Insert(string text) method of RadRichTextBox and RadDocumentEditor. Having inserted the string, it will naturally be included in the HTML export.
I hope this answers your question.
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