I'm not sure which library you are using for the translation and why it works like that,but I will try to answer your question anyway.
If you are interested to store form values whenever the language is changed, you can simply hook into the language change event.
For instance with ngx-translate you can simply hook to the onLangChange event.
onLangChange.subscribe((event: LangChangeEvent) => {
const formValue = this.form.value
// Persist form value into the localStorage
});
Another option is to simply persist your form values to the localStorage whenever a change is made to the form. Like (DerrickF suggested)
That way you will always have the latest form value:
this.form.valueChanges.subscribe(formValue=> // Persist to local storage)
and you can simply load them from localStorage and set the form value with
this.form.setValue(**yourPersistedFormValue**)