Please keep in mind that only received messages can be saved in your profile.
To save a received message in your profile permanently, just click in the message and select 'Save'.
You can also forward an entire chat to your email address. To do so, open the chat (chat-bubble, top-right), select the conversation in question, click on the three dots (top-left) and select "Forward to my email".
In general, unsaved received messages that you have read will be automatically deleted after 7 days. Unread messages will be deleted from your profile after 2 weeks. At the same time they will be forwarded to your email address, provided you have verified it.
As a PLUS user, you can use your own phrases and send them in all your conversations. Tap on the plus icon ⊕ next the text field of your chat and select 'Saved phrases' > 'Add' > type your phrase > 'Save'. Now your saved sentence is available in all your chats by tapping on the plus icon ⊕ > 'Saved phrases'. If you select 'Edit', you can change your existing saved phrases (tap on the phrase to change > apply the changes > 'Save') or delete them (garbage bin icon). There is one default phrase that is usable also by free accounts: the so-called "no thanks" phrase, that you can use to politely say "no" to users that are not a match for you.