You can only give private album access to another member within a conversation. You can either add it to a Conversation you started, or when replying to a Conversation.
In Messenger, if you are already having a Conversation with another member, just click on the picture icon on the left hand side of the text input area. The option to attach your album/s will appear. The album/s will then appear in the Conversation and can be clicked to view right away.
If you are starting a Conversation via someone's open profile page, then the process is similar but please click on the three dots icon to reveal the picture icon.
On the App or mobile web version of RedHotPie, the process is similar but you will need to click on the camera icon, or if hidden while typing, click on the green arrow icon to reveal the camera icon. Select the album/s you wish to share and send.