If you publish a Multi-Line textbox from InfoPath to a SharePoint column, you might discover that the text cuts off after 255 characters.  This is because InfoPath maps the textbox control to a “single line of text” column type regardless of whether the InfoPath textbox is mutli-line or single.

The work around for this is to manually create a “multiple lines of text” column type in the destination library and then CHANGE the InfoPath field mapping to this new column.  Before you begin you must have already published the form to a SharePoint library and included the InfoPath multi-line text field in the published columns.  Once this has been done go to your SharePoint form library and create a Multiple lines of text column:

I usually just add the word “Text” to the end of the column name to make it unique.  So if the InfoPath field was named “Request Info”, I would name the SharePoint column “Request Info Text” to make it unique.

Choose the Multiple Lines of text option.  Check the Yes button to allow unlimited length in document libraries.  Click on the OK button.

Now go to your InfoPath form, choose the top File tab, the side Publish tab, and click on the SharePoint Server button.

Since we have already setup the publishing settings to the SharePoint Library before we started, just hit Next for the Location, Next for the Type of Form, Next for the location of the form, and you should see the list of Columns:

Highlight the InfoPath multi-line field name (Request Info) and click Modify.  From the Column Name dropdown box select the new SharePoint multi-line column (Request Info Text) and click OK.  You have now mapped the InfoPath field (Request Info) to a multi-line SharePoint column (Request Info Text).  Click Next and then Publish to complete the wizard.