Let's Encrypt works fine, only not with file_get_contents()

Some data:
- ISPConfig Version: 3.1.15p2
- Ubuntu 16.04 (up-to-date) (php 7.0.33-0ubuntu0.16.04.7)
- Set up with the Perfect Server tutorial (thanks for that!)
- site configuration:
SuExec on, Own Error-Documents on, Auto-Subdomain www, SSL on, Let's Encrypt SSL on, PHP: Fast-CGI, PHP version default

This works fine in browsers. There is a PHP script on the server that tries to access its own frontend using file_get_contents(). This produces some errors:
Core: Error handler (BE): PHP Warning: file_get_contents(http://www.bordercollies.nl/index.php?id=71&L=0): failed to open stream: operation failed in /web/typo3conf/ext/solr/Classes/IndexQueue/PageIndexerRequest.php line 407
Core: Error handler (BE): PHP Warning: file_get_contents(): Failed to enable crypto in /web/typo3conf/ext/solr/Classes/IndexQueue/PageIndexerRequest.php line 407
Core: Error handler (BE): PHP Warning: file_get_contents(): SSL operation failed with code 1. OpenSSL Error messages: error:14090086:SSL routines:ssl3_get_server_certificate:certificate verify failed in /web/typo3conf/ext/solr/Classes/IndexQueue/PageIndexerRequest.php line 407

These errors are produced consistently with various URLs. If I request the same URLs with wget the contents are retrieved without errors.
Next, verification with openssl:
# openssl s_client -servername bordercollies.nl -connect bordercollies.nl:443 </dev/null
CONNECTED(00000003)
depth=2 O = Digital Signature Trust Co., CN = DST Root CA X3
verify return:1
depth=1 C = US, O = Let's Encrypt, CN = Let's Encrypt Authority X3
verify return:1
depth=0 CN = bordercollies.nl
verify return:1
---
Certificate chain
0 s:/CN=bordercollies.nl
i:/C=US/O=Let's Encrypt/CN=Let's Encrypt Authority X3
1 s:/C=US/O=Let's Encrypt/CN=Let's Encrypt Authority X3
i:/O=Digital Signature Trust Co./CN=DST Root CA X3
---
Server certificate
-----BEGIN CERTIFICATE-----
MIIGbzCCBVegAwIBAgISA/wKd40IDqAURGDiioe5EWV9MA0GCSqGSIb3DQEBCwUA
[...]
9WvUob9WTyXWEOqbVpHxSMhYqA==
-----END CERTIFICATE-----
subject=/CN=bordercollies.nl
issuer=/C=US/O=Let's Encrypt/CN=Let's Encrypt Authority X3
---
No client certificate CA names sent
Peer signing digest: SHA512
Server Temp Key: ECDH, P-256, 256 bits
---
SSL handshake has read 3795 bytes and written 456 bytes
---
New, TLSv1/SSLv3, Cipher is ECDHE-RSA-AES256-GCM-SHA384
Server public key is 4096 bit
Secure Renegotiation IS supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
Protocol : TLSv1.2
Cipher : ECDHE-RSA-AES256-GCM-SHA384
Session-ID: ACBE3B84C3DF889D54[...]9EDCA649C560E6247EF7
Session-ID-ctx:
Master-Key: E653B6F7239041BE93[...]F5DF7D9FF09DFFC9CAF
Key-Arg : None
PSK identity: None
PSK identity hint: None
SRP username: None
TLS session ticket lifetime hint: 300 (seconds)
TLS session ticket:
0000 - 6d b0 ea 67 66 72 aa 10-b8 d1 4e b7 05 9d 49 f1 m..gfr....N...I.
[...]
00c0 - 6d 32 78 bc 65 38 2e 93-dd 49 89 bd f0 d0 83 12 m2x.e8...I......

Start Time: 1578525021
Timeout : 300 (sec)
Verify return code: 0 (ok)
---
DONE

Let's Encrypt certificate seems fine, but somehow PHP doesn't accept it. Is there something missing in the PHP configuration?

Thanks for any ideas to solve this!

Regards, Jigal.