On making the TransactionSearch request I receive the list of the transactions with the TRANSACTIONID field for the transactions, corresponding to the recurring payments, in the form e.g. "I-BRPN2RUD8W0G" (current is fake).
For the rest transactions - I get usual 17 single-byte alphanumeric string. That means, that for recurring payments PayPal returns ProfileID, but not TransactionID.
As a result when I request the GetTransactionDetails with this transaction id passed to PayPal I receive valid details for ordinary payments and ERROR with the message "The transaction id is not valid" for the case of recurring payments.