You republish a book from 1923 without asking anyone.
The original publisher (or its successor) sues you.
Do you need to proof that the author is 70 years dead already, or lies the burden of proof on the publisher?
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The person suing (Plaintiff) needs to make a case that is prima facie reasonable and contains all needed details. This includes showing that they own a valid copyright/exclusive usage license - which is established by showing the trail of holders of the right from the work's creation to now. Because copyrights expire after the death of the author, a valid copyright upon which a descendent could sue would require showing that less than 70 years after the author's death have passed. They could show so trivially by showing the death certificate of the author, proving that the author died at most 70 years ago.
If the defendant tries to claim that the copyright is expired, it is upon the defendant to prove this. It would be upon the defendant to prove that the work was made by someone that passed more than 70 years ago at the time of the alleged copyright violation.
In general, in a civil claim, it is upon the moving party to offer up facts that support their claim.
Short answer: §§ 64 ff. UrhG is not a defense (Einwendung) but an integral/constitutional component of copyright. Accordingly the party favoring the fact that a work is (still) copyrighted has the burden of proof.
Long answer: Copyright cases are divided into four steps:
In a civil action suit parties need to present facts, § 282 ZPO (Beibringungsgrundsatz). The court/state does not investigate anything. That means the plaintiff contending that he has a claim for damages needs to demonstrate that it’s a copyrightable work, they are the copyright holder, and you infringed their rights. For the last item you may face an obligation to disclose certain evidence as per §§ 101 ff. UrhG.
The plaintiff can actually simply claim anything; until you dispute their claims it is believed to be true, § 138 Ⅲ, 288 ZPO. Yet still, lying about hard facts is forbidden, § 138 Ⅰ ZPO (Wahrheitspflicht). Claiming the work’s creator was alive in 1952 even though they very well know he was not is illegal.
On the other hand since you are relying on §§ 64/65 Ⅰ, 129 Ⅰ 1 UrhG, that is the circumstance copyright has expired 70 complete calendar years after the (last co)author’s death, § 69 UrhG, you will need to contest any claim copyright did not expire (subjektive Behauptungslast). No copyright protection → no damages. Otherwise it is believed there was no issue about this.
The plaintiff will then again need to produce evidence that copyright has not expired. It is the plaintiff who seeks damages under § 97 Ⅱ 1 UrhG so they have the burden of proof regarding all requirements of this legal basis.