First, if you recorded the Output of the Arpeggiators as MIDI Events to the DAW (Cubase) you should refer to the data as MIDI Track events — in other words, they should no longer be referred to as Arpeggio data.

After you transfer the Arpeggio Phrase data to recorded MIDI Events, turn the the Master Arp On/Off switch = Off.
And set the individual Part Arp On/Off switches = Off
Press [STORE] with the Arp Switches set to Off.
When both the Master and all Part Arp Switches are Off, all data will playback as recorded to the Tracks, as MIDI Events.

If you are running MODX CONNECT inside of Cubase.
Make sure “Auto Sync” = On, this will ensure that when you SAVE your Cubase data it will capture your Performance and bundle it with the Cubase Project File (.CPR).
When next you open the Cubase Project, it will restore your MODX Performance with all the Arp Switches properly set to Off.

If your goal is to play along with your finished sequencer be sure to STORE your Performance with the correct start condition... with the KBD CTRL icon(s) active (green) on the Part(s) you wish to sound when you interact with the Keys. Also make sure you restore LOCAL CONTROL = On.

It is standard operating procedure to work with Local Control = Off when recording MIDI data yo a computer sequencer — this allows routing and channel designation to be determined in the DAW sofware. Return Local Control On when you wish the MODX Keyboard to communicate normally with its Tone Generator

Extra Credit:
You can bypass the Arpeggiator’s entirely by pressing [SHIFT] + [MASTER ARP ON/OFF] — the Master Arp button will flash indicating it is bypassed (useful before finalizing your Performance).

Learn to read the “MIDI Signal Flow” diagrams.
They will show you the position of the Arpeggiator in the response to your current settings.
The Arpeggiator is located between the “Keyboard” and the “Tone Generator”.

You can see where Local Control if set to OFF, forces the Key press data to go to “MIDI OUT” without reaching the Tone Generator.
Instead it goes to the DAW (Cubase) MIDI Track.
When routed back to the MODX by the MIDI Track, it arrives at “MIDI IN” where it can trigger the Arpeggiator just before the Tone Generator.

Turn “Arp MIDI Out” = On

Understand that turning the “Arp MIDI Out” parameter On and Off is actually moving the position of the Arpeggio block. While viewing the “MIDI Settings” screen shown above toggle the “Arp MIDI Out” OFF and then On, to gain an understanding of the Arpeggiator block’s position... and how it impacts the results.

Understand that the Arpeggiator block prevents note-on events from traveling farther along — it applies the assigned data... by blocking the trigger notes and sending a note phrase through to the next device... or it will allow the trigger notes to pass while it applies a Control Change or Pitch Bend message stored in the Arp Phrase.

The position of the Arpeggio block can only be involved with the Cubase MIDI Track when it is located post (after) the MIDI IN and pre (before) the Tone Generator.
When “MIDI I/O Mode” = Single or Hybrid, the Arpeggiator is locked in position between the MIDI IN and the Tone Generator. Arpeggio data cannot be output in either Single or Hybrid Modes

Hello Bad Mister,

many thanks for your information on how to record arpeggio data in Cubase.
Unfortunately, it doesn`t work in this case, because I use data already recorded in MODX and then imported in Cubase.
I have the arpeggio buttons all switched "off", but when running the song in Cubase the main arp-button is automatically switched to "on" every time the imported parts are started.
I asume I have to delete some hidden order in the track to not to be send to MODX.
Am I right?

... I have the arpeggio buttons all switched "off", but when running the song in Cubase the main arp-button is automatically switched to "on" every time the imported parts are started.

What is an “imported part”?

Please describe how it is different from a regular MODX Part stored in a Performance.

I asume I have to delete some hidden order in the track to not to be send to MODX.
Am I right?

This is yet to be determined.

Are you using MODX CONNECT to recall the Performance?
If yes, then turn the Master Arp On/Off = Off before Saving the Cubase Project.

If not, then please describe what you are doing a bit better, thanks.