Thunderbird has the feature to add further identities that are linked to en existing e-mail account.
To add your "synonym" (I would call it an alias) account open the "Account settings" and select your GMX account. On the right side near the bottom there is a button "Manage Identities". It opens a dialog that allows to specify multiple alias accounts.
When writing a new e-mail you can select the new alias identity by clicking on the "From" entry - it will open a drop-down combo box showing all your mail identities and alias identities
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