In order to transport texts from SO10 transaction you can use the standard report RSTXTRAN. You have to be patient because it is a very very old report.
Complete the selection screen with the task (no the transport order, the task) and execute F8.
Standard report RSTXTRAN
RSTXTRAN – Add of SAPscript Texts to Correction
An horrible ALV will appears with the text. Press ENTER in order to confirm.
A new button appears in the top. Press it and confirm the pop-up. Finally a confirmation message will appears.
An that’s all!